Finite Group Databasebeta

← #14774607

Subgroups — #14774607

Order 2816.

998 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077460C212yesmaximal, complemented
2#13077149C212yesmaximal
3#13069419C211yesmaximal, characteristic, complemented
4#13069273C212yesmaximal, complemented
5#13069133C212yesmaximal, complemented
6#13069010C211yesmaximal, characteristic, complemented
7#13068844C212yesmaximal, complemented
8#13068454C212yesmaximal, complemented
9C2×C11×#456C211yesmaximal, characteristic
10C2×C11×2−1+4C2211yescharacteristic
11C2×C11×#137C2212yes—
12C2×C11×C4⋊Q8C2211yescharacteristic
13#10623358C2212yes—
14C2×#67001C2212yes—
15#10623343C2211yescharacteristic
16C11×#456C418yescomplemented
17C2×C11×#104C2212yes—
18C2×C11×#101C2211yescharacteristic
19#10622846—22no—
20#10622846C2212yes—
21#10622845—22no—
22#10622845C2212yes—
23C2×#66900C2211yescharacteristic
24#10622838—22no—
25#10622838C2212yes—
26C2×#66899—22no—
27C2×#66899C2212yes—
28C2×#66899C2212yes—
29#10622797—22no—
30Q16×Dic11—22no—
31#10622777—22no—
32SD16×Dic11—22no—
33#10622735C2212yes—
34#10622734C2212yes—
35#10622548C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622196C2212yes—
38#10622192C2212yes—
39#10622161C2212yes—
40C11×2−1+4—24no—
41C11×2−1+4—41no—
42C11×2−1+4C2×C414yes—
43C2×C11×#41—22no—
44C2×C11×#41—41no—
45C2×C11×#41C2312yes—
46C22×Q8×C11—22no—
47C22×Q8×C11C2311yescharacteristic
48C22×Q8×C11C2311yescharacteristic
49C11×#137—24no—
50C11×#137C2×C418yescomplemented
51C2×C11×Q16—22no—
52C2×C11×SD16—22no—
53C2×C11×M16C2312yes—
54C11×C4⋊Q8—41no—
55C11×C4⋊Q8C2×C414yescomplemented
56C2×C11×C4⋊C4—41no—
57C2×C42×C11C2311yescharacteristic
58#67001—24no—
59#67001—42no—
60Q8×Dic11—22no—
61Q8×Dic11—22no—
62Q8×Dic11—22no—
63D4×Dic11—22no—
64D4×Dic11—42no—
65#66979—22no—
66#66979—41no—
67#66979C2312yes—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—41no—
70C2×C4⋊Dic11C2312yes—
71C2×#4318—22no—
72C2×#4318C2312yes—
73C22×C11⋊C8—22no—
74C22×C11⋊C8C2312yes—
75C11×#104C2×C418yescomplemented
76C11×#101C2×C414yescomplemented
77#66900—41no—
78#66899—22no—
79#66899—22no—
80#66899—22no—
81#66899—22no—
82#66899—22no—
83#66899—22no—
84#66899—22no—
85#66899D412yes—
86#66899D412yes—
87#66896—22no—
88#66896D412yes—
89#66896D412yes—
90#66882—22no—
91#66881—22no—
92#66879—22no—
93C8×Dic11—22no—
94C4×C11⋊C8—41no—
95#22894—111nomaximal, Sylow
96C11×#41—22no—
97C11×#41—22no—
98C11×#41—28no—
99C11×#41—44no—
100C11×#41—44no—
101C11×#41—44no—
102C11×#41C22×C414yes—
103C11×#41#4114yes—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—28no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—41no—
112C2×Q8×C11—44no—
113C2×Q8×C11C22×C412yes—
114C2×Q8×C11C22×C412yes—
115C2×Q8×C11C2×D412yes—
116C2×D4×C11—22no—
117C2×D4×C11—41no—
118C2×D4×C11C2×D412yes—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—42no—
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—22no—
126C22×Dic11—42no—
127C11×Q16—28no—
128C11×SD16—28no—
129C11×M16—22no—
130C11×M16C22×C414yes—
131C2×C8×C11—22no—
132C11×C4⋊C4—44no—
133C42×C11—21no—
134C42×C11C22×C412yes—
135C22⋊Dic11—22no—
136C22⋊Dic11—42no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11—42no—
140C4⋊Dic11—41no—
141C4⋊Dic11—41no—
142C4⋊Dic11—82no—
143C4⋊Dic11C2×D412yes—
144C4⋊Dic11C2×D412yes—
145C4×Dic11—22no—
146C4×Dic11—42no—
147C4×Dic11—42no—
148#4318—22no—
149#4318—22no—
150#4318—44no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—44no—
155C2×C11⋊C8C2×D412yes—
156C2×C11⋊C8C2×D412yes—
157C2×#456D1111yescharacteristic
158#2947—112no—
159#2898—112no—
160#1956—111no—
161#1930—112no—
162#1908—112no—
163#1886—111no—
164#1859—112no—
165#1764—112no—
166C23×C11—22no—
167C23×C11H(5,𝔽2)11yescharacteristic
168Q8×C11—22no—
169Q8×C11—24no—
170Q8×C11—24no—
171Q8×C11—44no—
172Q8×C11—42no—
173Q8×C11—42no—
174Q8×C11C4×D414yes—
175D4×C11—24no—
176D4×C11—24no—
177D4×C11—22no—
178D4×C11—44no—
179D4×C11C4×D414yes—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—48no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11C23×C411yescharacteristic
194C2×C4×C11C22×D412yes—
195C2×C4×C11C2×#4112yes—
196C2×C4×C11H(5,𝔽2)11yescharacteristic
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—42no—
200C2×Dic11—82no—
201C2×Dic11—162no—
202C8×C11—24no—
203C11⋊C8—22no—
204C11⋊C8—22no—
205C11⋊C8—42no—
206C2×2−1+4C2×D1111yescharacteristic
207C2×#137C2×D1112yes—
208C2×#131—112no—
209C2×C4⋊Q8C2×D1111yescharacteristic
210#520—112no—
211#519—111no—
212#456Dic1118yescomplemented
213#441—222no—
214#440—222no—
215C4×Q16—222no—
216C4×SD16—222no—
217#428—112no—
218C2×#104C2×D1112yes—
219#419—112no—
220#419—222no—
221#417—112no—
222#417—222no—
223#416—112no—
224#416—222no—
225C2×#103—112no—
226C2×#103—112no—
227C2×#103—222no—
228C2×#101—111no—
229C2×#101C2×D1111yescharacteristic
230#405—112no—
231C2×C4×C8—111no—
232#384—111no—
233#343—112no—
234#341—112no—
235#339—112no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—24no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11#51811yescharacteristic
242C22×C11D4211yescharacteristic
243C22×C11#55111yescharacteristic
244C4×C11—24no—
245C4×C11—24no—
246C4×C11—42no—
247C4×C11—42no—
248C4×C11C2×C4×D412yes—
249C4×C11#54612yes—
250Dic11—42no—
251Dic11—42no—
252Dic11—82no—
2532−1+4—24no—
2542−1+4—41no—
2552−1+4C2×Dic1114yes—
256C2×#41—22no—
257C2×#41—41no—
258C2×#41C22×D1112yes—
259C22×Q8—22no—
260C22×Q8C22×D1111yescharacteristic
261C22×Q8C22×D1111yescharacteristic
262#137—24no—
263#137C2×Dic1118yescomplemented
264C2×Q16—22no—
265C2×SD16—22no—
266#131—224no—
267#131—442no—
268C2×M16—112no—
269C2×M16—222no—
270C2×M16C22×D1112yes—
271C22×C8—112no—
272C22×C8—222no—
273C4⋊Q8—41no—
274C4⋊Q8C2×Dic1114yescomplemented
275C4×Q8—222no—
276C4×Q8—222no—
277C4×Q8—222no—
278C4×D4—222no—
279C4×D4—442no—
280#117—112no—
281#117—222no—
282#117—441no—
283C2×C4⋊C4—41no—
284C2×C4⋊C4—112no—
285C2×C4⋊C4—222no—
286C2×C4⋊C4—441no—
287C2×C42C22×D1111yescharacteristic
288#107—222no—
289#106—222no—
290#104C2×Dic1118yescomplemented
291#103—112no—
292#103—112no—
293#103—222no—
294#103—222no—
295#103—222no—
296#103—222no—
297#103—222no—
298#103—222no—
299#103—222no—
300#102—112no—
301#102—112no—
302#102—222no—
303#101—441no—
304#101C2×Dic1114yescomplemented
305#97—222no—
306C4×C8—222no—
307C4×C8—441no—
308C2×C11—21no—
309C2×C11—21no—
310C2×C11—44no—
311C2×C11#235811yescharacteristic
312C2×C11#329111yescharacteristic
313C2×C11#329311yescharacteristic
314#41—22no—
315#41—22no—
316#41—28no—
317#41—44no—
318#41—44no—
319#41—44no—
320#41#434114yes—
321#41C22×Dic1114yes—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×Q8—28no—
325C2×Q8—22no—
326C2×Q8—22no—
327C2×Q8—22no—
328C2×Q8—22no—
329C2×Q8—41no—
330C2×Q8—44no—
331C2×Q8D4×D1112yes—
332C2×Q8C22×Dic1112yes—
333C2×Q8C22×Dic1112yes—
334C2×D4—22no—
335C2×D4—41no—
336C2×D4D4×D1112yes—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—42no—
342C22×C4—222no—
343C22×C4—442no—
344C22×C4C23×D1111yescharacteristic
345Q16—28no—
346SD16—28no—
347M16—22no—
348M16—222no—
349M16—222no—
350M16—444no—
351M16C22×Dic1114yes—
352C2×C8—22no—
353C2×C8—112no—
354C2×C8—112no—
355C2×C8—222no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8—444no—
359C4⋊C4—44no—
360C4⋊C4—112no—
361C4⋊C4—112no—
362C4⋊C4—222no—
363C4⋊C4—222no—
364C4⋊C4—442no—
365C4⋊C4—441no—
366C4⋊C4—441no—
367C4⋊C4—882no—
368C22⋊C4—222no—
369C22⋊C4—442no—
370C42—21no—
371C42—222no—
372C42—442no—
373C42—442no—
374C42C22×Dic1112yes—
375C11#2289411yescharacteristic, complemented, Sylow
376C23—22no—
377C23#6703711yescharacteristic
378Q8—22no—
379Q8—24no—
380Q8—24no—
381Q8—44no—
382Q8—42no—
383Q8—42no—
384Q8D4×Dic1114yes—
385D4—24no—
386D4—24no—
387D4—22no—
388D4—44no—
389D4D4×Dic1114yes—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—48no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—222no—
404C2×C4—222no—
405C2×C4—442no—
406C2×C4—882no—
407C2×C4—1762no—
408C2×C4C2×D4×D1112yes—
409C2×C4C2×#434112yes—
410C2×C4#6703711yescharacteristic
411C2×C4C23×Dic1111yescharacteristic
412C8—24no—
413C8—222no—
414C8—222no—
415C8—442no—
416C22—21no—
417C22—21no—
418C22—24no—
419C22—42no—
420C22—42no—
421C22#1062311811yescharacteristic
422C22#1062312111yescharacteristic
423C22#1062332911yescharacteristic
424C4—24no—
425C4—24no—
426C4—42no—
427C4—42no—
428C4—442no—
429C4—442no—
430C4—882no—
431C4#1062312212yes—
432C4C2×D4×Dic1112yes—
433C2—21no—
434C2—21no—
435C2—44no—
436C2#1307160011yescharacteristic
437C2#1308040611yescharacteristic
438C2#1308041711yescharacteristic
subgroupG/H
centerC22#10623121
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#456C2
socleC22×C11D42
prime radicalC2×C11×2−1+4C22
cosocleC22×C4×C11C24
hypercenterC2×#456D11
hypocenterC11#22894
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#456

Complements

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

NH ≅ G/Ntype
1. #13077460C2semidirect
3. #13069419C2semidirect
4. #13069273C2semidirect
5. #13069133C2semidirect
6. #13069010C2semidirect
7. #13068844C2semidirect
8. #13068454C2semidirect
16. C11×#456C4semidirect
50. C11×#137C2×C4semidirect
55. C11×C4⋊Q8C2×C4semidirect
75. C11×#104C2×C4semidirect
76. C11×#101C2×C4semidirect
212. #456Dic11semidirect
263. #137C2×Dic11semidirect
274. C4⋊Q8C2×Dic11semidirect
290. #104C2×Dic11semidirect
304. #101C2×Dic11semidirect
375. C11#22894semidirect

Maximal subgroups

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

subgroupindex
#130774602
#130771492
#130694192
#130692732
#130691332
#130690102
#130688442
#130684542
C2×C11×#4562
#2289411