Finite Group Databasebeta

← #14767633

Subgroups — #14767633

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071336C211yesmaximal, characteristic, complemented
2#13071329C211yesmaximal, characteristic
3#13069428C211yesmaximal, characteristic
4#13069419C211yesmaximal, characteristic, complemented
5#13068973C212yesmaximal
6#13068959C212yesmaximal, complemented
7#13068959C212yesmaximal, complemented
8#13068952C212yesmaximal
9#13068750C211yesmaximal, characteristic, complemented
10#13068369C211yesmaximal, characteristic, complemented
11C2×C11×#497C211yesmaximal, characteristic
12C22×C11×Q16C2212yes—
13C22×C11×SD16C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#124C2211yescharacteristic
16C2×Q8×Dic11C2211yescharacteristic
17C2×Q8×Dic11C2212yes—
18C2×D4×Dic11C2211yescharacteristic
19C11×#497C418yescomplemented
20C2×C11×#97C2211yescharacteristic
21#10622843C2212yes—
22#10622843C2211yescharacteristic
23C2×#66899C2212yes—
24C2×#66899C2212yes—
25C2×#66899C2212yes—
26#10622834C2211yescharacteristic
27C2×#66896C2212yes—
28#10622594—22no—
29#10622594—22no—
30#10622564—22no—
31#10622563—22no—
32#10622549C2211yescharacteristic
33#10622548C2211yescharacteristic
34#10622545C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622189C2212yes—
37#10622189C2212yes—
38#10622188C2212yes—
39#10622188C2212yes—
40C22×Q8×C11C2311yescharacteristic
41C22×Q8×C11C2312yes—
42C22×D4×C11C2311yescharacteristic
43C23×Dic11—21no—
44C2×C11×Q16—42no—
45C2×C11×Q16—42no—
46C2×C11×Q16C2×C418yescomplemented
47C2×C11×SD16—42no—
48C2×C11×SD16—42no—
49C2×C11×SD16C2×C418yes—
50C22×C8×C11C2312yes—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8C2×C414yescomplemented
53C11×#124—22no—
54C11×#124C2×C414yes—
55C2×C11×C4⋊C4—22no—
56C2×C11×C22⋊C4—22no—
57C2×C42×C11C2311yescharacteristic
58C2×C22⋊Dic11—21no—
59C2×C22⋊Dic11—22no—
60Q8×Dic11—42no—
61Q8×Dic11—42no—
62Q8×Dic11—42no—
63D4×Dic11—42no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2312yes—
70C2×C4×Dic11—21no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11C2311yescharacteristic
73C2×C4×Dic11C2311yescharacteristic
74C22×C11⋊C8C2312yes—
75C11×#97C2×C414yescomplemented
76#66899—42no—
77#66899—42no—
78#66899—42no—
79#66896—42no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95D412yes—
85C11⋊#95D412yes—
86C4×C11⋊C8—22no—
87#22278—111nomaximal, Sylow
88C24×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11C22×C412yes—
98C2×Q8×C11C22×C414yes—
99C2×D4×C11—21no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11C22×C412yes—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—22no—
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—42no—
111C22×Dic11—82no—
112C22×Dic11C2×D411yescharacteristic
113C22×Dic11C2×D411yescharacteristic
114C22×Dic11C2×D412yes—
115C11×Q16—48no—
116C11×SD16—48no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11C22×C414yes—
120C11×C4⋊C4—28no—
121C11×C22⋊C4—28no—
122C42×C11C22×C412yes—
123C42×C11#4112yes—
124C22⋊Dic11—42no—
125C22⋊Dic11—82no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—44no—
131C4⋊Dic11—42no—
132C4⋊Dic11—82no—
133C4×Dic11—22no—
134C4×Dic11—22no—
135C4×Dic11—44no—
136C4×Dic11—42no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×#497D1111yescharacteristic
141#2327—111no—
142#2326—111no—
143#1958—111no—
144#1956—111no—
145#1880—112no—
146#1878—112no—
147#1878—112no—
148#1877—112no—
149#1836—111no—
150#1746—111no—
151C23×C11—22no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—42no—
155C23×C11—42no—
156C23×C11C22×D411yescharacteristic
157Q8×C11—24no—
158Q8×C11—24no—
159Q8×C11—24no—
160Q8×C11—42no—
161Q8×C11—42no—
162Q8×C11—42no—
163D4×C11—24no—
164D4×C11—42no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—24no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11C4×D414yes—
174C2×C4×C11C23×C411yescharacteristic
175C2×C4×C11C2×#4111yescharacteristic
176C2×C4×C11H(5,𝔽2)12yes—
177C2×C4×C11H(5,𝔽2)12yes—
178C2×Dic11—22no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—22no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—41no—
186C2×Dic11—42no—
187C2×Dic11—41no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—84no—
193C8×C11—24no—
194C11⋊C8—42no—
195C22×Q16C2×D1112yes—
196C22×SD16C2×D1112yes—
197C2×C4⋊Q8C2×D1111yescharacteristic
198C2×#124C2×D1111yescharacteristic
199C2×C4×Q8—111no—
200C2×C4×Q8—112no—
201C2×C4×D4—111no—
202#497Dic1118yescomplemented
203C2×#103—112no—
204C2×#103—112no—
205C2×#103—112no—
206C2×#102—112no—
207C2×#97C2×D1111yescharacteristic
208C2×C4×C8—111no—
209#391—111no—
210#391—112no—
211#390—111no—
212#388—222no—
213#387—222no—
214#387—222no—
215#385—222no—
216#384—111no—
217#382—111no—
218#376—111no—
219#340—112no—
220#340—112no—
221#336—112no—
222#336—112no—
223C22×C11—42no—
224C22×C11—44no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11—82no—
228C22×C11C2×C4×D411yescharacteristic
229C22×C11#53511yescharacteristic
230C22×C11#53511yescharacteristic
231C22×C11#57712yes—
232C22×C11#57812yes—
233C4×C11—24no—
234C4×C11—42no—
235C4×C11—44no—
236C4×C11#51812yes—
237C4×C11#54012yes—
238Dic11—41no—
239Dic11—41no—
240Dic11—42no—
241Dic11—81no—
242Dic11—81no—
243Dic11—82no—
244C22×Q8C22×D1111yescharacteristic
245C22×Q8C22×D1112yes—
246C22×D4C22×D1111yescharacteristic
247C23×C4—221no—
248C2×Q16—42no—
249C2×Q16—42no—
250C2×Q16C2×Dic1118yescomplemented
251C2×SD16—42no—
252C2×SD16—42no—
253C2×SD16C2×Dic1118yes—
254C22×C8—112no—
255C22×C8C22×D1112yes—
256C4⋊Q8—22no—
257C4⋊Q8C2×Dic1114yescomplemented
258#124—22no—
259#124C2×Dic1114yes—
260C4×Q8—442no—
261C4×Q8—442no—
262C4×Q8—442no—
263C4×D4—442no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—112no—
267C2×C4⋊C4—111no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—222no—
270C2×C4⋊C4—222no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—221no—
273C2×C22⋊C4—222no—
274C2×C42—111no—
275C2×C42—111no—
276C2×C42—222no—
277C2×C42—221no—
278C2×C42C22×D1111yescharacteristic
279#103—442no—
280#103—442no—
281#103—442no—
282#102—442no—
283#97C2×Dic1114yescomplemented
284C4×C8—222no—
285#95—112no—
286#95—112no—
287#95—222no—
288#95—222no—
289#95—222no—
290#95—222no—
291C2×C11—82no—
292C2×C11#232811yescharacteristic
293C2×C11#294712yes—
294C2×C11#322211yescharacteristic
295C2×C11#322311yescharacteristic
296C2×C11#322512yes—
297C24—21no—
298C2×Q8—21no—
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8—22no—
305C2×Q8—22no—
306C2×Q8C22×Dic1112yes—
307C2×Q8C22×Dic1114yes—
308C2×D4—21no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4C22×Dic1112yes—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—111no—
315C22×C4—111no—
316C22×C4—112no—
317C22×C4—222no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—442no—
321C22×C4—882no—
322C22×C4D4×D1112yes—
323C22×C4C23×D1111yescharacteristic
324Q16—48no—
325SD16—48no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—222no—
329C2×C8—222no—
330C2×C8—222no—
331C2×C8C22×Dic1114yes—
332C4⋊C4—28no—
333C4⋊C4—222no—
334C4⋊C4—222no—
335C4⋊C4—222no—
336C4⋊C4—222no—
337C4⋊C4—444no—
338C4⋊C4—442no—
339C4⋊C4—882no—
340C22⋊C4—28no—
341C22⋊C4—442no—
342C22⋊C4—882no—
343C42—222no—
344C42—222no—
345C42—442no—
346C42—444no—
347C42#434112yes—
348C42C22×Dic1112yes—
349C11#2227811yescharacteristic, complemented, Sylow
350C23—22no—
351C23—41no—
352C23—41no—
353C23—42no—
354C23—42no—
355C23C2×D4×D1111yescharacteristic
356Q8—24no—
357Q8—24no—
358Q8—24no—
359Q8—42no—
360Q8—42no—
361Q8—42no—
362D4—24no—
363D4—42no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—24no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—221no—
373C2×C4—222no—
374C2×C4—221no—
375C2×C4—222no—
376C2×C4—222no—
377C2×C4—222no—
378C2×C4—222no—
379C2×C4—441no—
380C2×C4—442no—
381C2×C4—441no—
382C2×C4—442no—
383C2×C4—442no—
384C2×C4—442no—
385C2×C4—442no—
386C2×C4—884no—
387C2×C4D4×Dic1114yes—
388C2×C4C2×#434111yescharacteristic
389C2×C4#6703712yes—
390C2×C4#6703712yes—
391C2×C4C23×Dic1111yescharacteristic
392C8—24no—
393C8—442no—
394C22—44no—
395C22—42no—
396C22—81no—
397C22—81no—
398C22—82no—
399C22#1062324611yescharacteristic
400C22#1062324611yescharacteristic
401C22#1062330912yes—
402C22#1062331012yes—
403C22C2×D4×Dic1111yescharacteristic
404C4—24no—
405C4—42no—
406C4—44no—
407C4—441no—
408C4—441no—
409C4—442no—
410C4—881no—
411C4—881no—
412C4—882no—
413C4#1062325012yes—
414C4#1062332912yes—
415C2—82no—
416C2#1307134211yescharacteristic
417C2#1307746012yes—
418C2#1307968311yescharacteristic
419C2#1307969411yescharacteristic
420C2#1307972012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#497C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC2×#497D11
hypocenterC11#22278
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. #13071336C2semidirect
4. #13069419C2semidirect
6. #13068959C2semidirect
7. #13068959C2semidirect
9. #13068750C2semidirect
10. #13068369C2semidirect
19. C11×#497C4semidirect
46. C2×C11×Q16C2×C4semidirect
52. C11×C4⋊Q8C2×C4semidirect
75. C11×#97C2×C4semidirect
202. #497Dic11semidirect
250. C2×Q16C2×Dic11semidirect
257. C4⋊Q8C2×Dic11semidirect
283. #97C2×Dic11semidirect
349. C11#22278semidirect

Maximal subgroups

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

subgroupindex
#130713362
#130713292
#130694282
#130694192
#130689732
#130689592
#130689522
#130687502
#130683692
C2×C11×#4972
#2227811