Finite Group Databasebeta

← #14774616

Subgroups — #14774616

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077449C212yesmaximal, complemented
2#13077149C212yesmaximal, complemented
3#13069428C211yesmaximal, characteristic, complemented
4#13069273C212yesmaximal, complemented
5#13069126C212yesmaximal, complemented
6#13069005C211yesmaximal, characteristic, complemented
7#13068851C212yesmaximal, complemented
8#13068454C212yesmaximal, complemented
9C2×C11×#454C211yesmaximal, characteristic
10C2×C11×2−1+4C2211yescharacteristic
11C2×C11×AGL(1,ℤ/8)C2212yes—
12C2×C11×#124C2211yescharacteristic
13#10623358C2212yes—
14C2×#67001C2212yes—
15#10623329C2211yescharacteristic
16C11×#454C418yescomplemented
17C2×C11×#104C2212yes—
18C2×C11×#101C2211yescharacteristic
19#10622846—22no—
20#10622846C2212yes—
21#10622845—22no—
22#10622845C2212yes—
23#10622838—22no—
24#10622838C2212yes—
25C2×#66899—22no—
26C2×#66899C2212yes—
27C2×#66897C2211yescharacteristic
28C2×#66896C2212yes—
29#10622777—22no—
30SD16×Dic11—22no—
31#10622765—22no—
32D8×Dic11—22no—
33#10622735C2212yes—
34#10622734C2212yes—
35#10622549C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622196C2212yes—
38#10622192C2212yes—
39#10622161C2212yes—
40C11×2−1+4—24no—
41C11×2−1+4—41no—
42C11×2−1+4C2×C414yescomplemented
43C2×C11×#41—22no—
44C2×C11×#41—41no—
45C2×C11×#41C2312yes—
46C22×Q8×C11—22no—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11C2311yescharacteristic
49C11×AGL(1,ℤ/8)—24no—
50C11×AGL(1,ℤ/8)C2×C418yescomplemented
51C2×C11×SD16—22no—
52C2×C11×D8—22no—
53C2×C11×M16C2312yes—
54C11×#124—41no—
55C11×#124C2×C414yescomplemented
56C2×C11×C22⋊C4—41no—
57C2×C42×C11C2311yescharacteristic
58C2×C22⋊Dic11—41no—
59#67001—24no—
60#67001—42no—
61Q8×Dic11—22no—
62D4×Dic11—22no—
63D4×Dic11—22no—
64D4×Dic11—22no—
65D4×Dic11—42no—
66#66979—22no—
67#66979C2312yes—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11C2312yes—
70C2×#4318—22no—
71C2×#4318C2312yes—
72C22×C11⋊C8—22no—
73C22×C11⋊C8C2312yes—
74C11×#104C2×C418yescomplemented
75C11×#101C2×C414yescomplemented
76#66899—22no—
77#66899—22no—
78#66899—22no—
79#66899—22no—
80#66899—22no—
81#66899D412yes—
82#66899D412yes—
83#66897—41no—
84#66896—22no—
85#66896—22no—
86#66896—22no—
87#66896D412yes—
88#66896D412yes—
89C11⋊#95—41no—
90#66882—22no—
91#66881—22no—
92#66879—22no—
93C8×Dic11—22no—
94C4×C11⋊C8—41no—
95#22895—111nomaximal, Sylow
96C24×C11—21no—
97C11×#41—22no—
98C11×#41—22no—
99C11×#41—28no—
100C11×#41—44no—
101C11×#41—44no—
102C11×#41—44no—
103C11×#41C22×C414yes—
104C11×#41#4114yes—
105C2×Q8×C11—21no—
106C2×Q8×C11—28no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—41no—
110C2×Q8×C11—44no—
111C2×Q8×C11C22×C412yes—
112C2×Q8×C11C2×D412yes—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—21no—
117C2×D4×C11—41no—
118C2×D4×C11C22×C412yes—
119C2×D4×C11C2×D412yes—
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—
127C22×Dic11—42no—
128C11×SD16—28no—
129C11×D8—28no—
130C11×M16—22no—
131C11×M16C22×C414yes—
132C2×C8×C11—22no—
133C11×C22⋊C4—44no—
134C42×C11—21no—
135C42×C11C22×C412yes—
136C22⋊Dic11—22no—
137C22⋊Dic11—42no—
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—42no—
143C4⋊Dic11C2×D412yes—
144C4⋊Dic11C2×D412yes—
145C4×Dic11—22no—
146C4×Dic11—42no—
147#4318—22no—
148#4318—22no—
149#4318—44no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—44no—
154C2×C11⋊C8C2×D412yes—
155C2×C11⋊C8C2×D412yes—
156C2×#454D1111yescharacteristic
157#2946—112no—
158#2898—112no—
159#1958—111no—
160#1930—112no—
161#1907—112no—
162#1885—111no—
163#1860—112no—
164#1764—112no—
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—82no—
170C23×C11H(5,𝔽2)11yescharacteristic
171Q8×C11—22no—
172Q8×C11—24no—
173Q8×C11—44no—
174Q8×C11—42no—
175Q8×C11C4×D414yes—
176D4×C11—24no—
177D4×C11—24no—
178D4×C11—24no—
179D4×C11—22no—
180D4×C11—44no—
181D4×C11—42no—
182D4×C11C4×D414yes—
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—42no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11C23×C411yescharacteristic
193C2×C4×C11C22×D412yes—
194C2×C4×C11C2×#4112yes—
195C2×C4×C11H(5,𝔽2)11yescharacteristic
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—42no—
199C2×Dic11—82no—
200C2×Dic11—162no—
201C2×Dic11—162no—
202C8×C11—24no—
203C11⋊C8—22no—
204C11⋊C8—22no—
205C11⋊C8—42no—
206C2×2−1+4C2×D1111yescharacteristic
207C2×AGL(1,ℤ/8)C2×D1112yes—
208C2×#131—112no—
209C2×#124C2×D1111yescharacteristic
210#520—112no—
211#518—111no—
212#454Dic1118yescomplemented
213#442—222no—
214#440—222no—
215C4×SD16—222no—
216C4×D8—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—222no—
227C2×#102—112no—
228C2×#101C2×D1111yescharacteristic
229C2×#100—111no—
230#405—112no—
231C2×C4×C8—111no—
232#382—111no—
233#343—112no—
234#341—112no—
235#339—112no—
236C22×C11—22no—
237C22×C11—24no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11—82no—
242C22×C11—82no—
243C22×C11—161no—
244C22×C11#51811yescharacteristic
245C22×C11D4211yescharacteristic
246C22×C11#55111yescharacteristic
247C4×C11—24no—
248C4×C11—42no—
249C4×C11—42no—
250C4×C11C2×C4×D412yes—
251C4×C11#54612yes—
252Dic11—42no—
253Dic11—42no—
254Dic11—82no—
2552−1+4—24no—
2562−1+4—41no—
2572−1+4C2×Dic1114yescomplemented
258C2×#41—22no—
259C2×#41—41no—
260C2×#41C22×D1112yes—
261C22×Q8—22no—
262C22×Q8C22×D1111yescharacteristic
263C22×D4C22×D1111yescharacteristic
264AGL(1,ℤ/8)—24no—
265AGL(1,ℤ/8)C2×Dic1118yescomplemented
266C2×SD16—22no—
267C2×D8—22no—
268#131—224no—
269#131—442no—
270C2×M16—112no—
271C2×M16—222no—
272C2×M16C22×D1112yes—
273C22×C8—112no—
274C22×C8—222no—
275#124—41no—
276#124C2×Dic1114yescomplemented
277C4×Q8—222no—
278C4×D4—222no—
279C4×D4—222no—
280C4×D4—222no—
281C4×D4—442no—
282#117—112no—
283#117—222no—
284C2×C4⋊C4—112no—
285C2×C4⋊C4—222no—
286C2×C22⋊C4—41no—
287C2×C22⋊C4—441no—
288C2×C42C22×D1111yescharacteristic
289#107—222no—
290#106—222no—
291#104C2×Dic1118yescomplemented
292#103—112no—
293#103—112no—
294#103—222no—
295#103—222no—
296#103—222no—
297#103—222no—
298#103—222no—
299#102—112no—
300#102—112no—
301#102—222no—
302#102—222no—
303#102—222no—
304#101C2×Dic1114yescomplemented
305#100—441no—
306#97—222no—
307C4×C8—222no—
308C4×C8—441no—
309#95—441no—
310C2×C11—21no—
311C2×C11—21no—
312C2×C11—44no—
313C2×C11—82no—
314C2×C11#235811yescharacteristic
315C2×C11#329012yes—
316C24—21no—
317#41—22no—
318#41—22no—
319#41—28no—
320#41—44no—
321#41—44no—
322#41—44no—
323#41#434114yes—
324#41C22×Dic1114yes—
325C2×Q8—21no—
326C2×Q8—28no—
327C2×Q8—22no—
328C2×Q8—22no—
329C2×Q8—41no—
330C2×Q8—44no—
331C2×Q8D4×D1112yes—
332C2×Q8C22×Dic1112yes—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—21no—
337C2×D4—41no—
338C2×D4D4×D1112yes—
339C2×D4C22×Dic1112yes—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—42no—
344C22×C4—222no—
345C22×C4—442no—
346C22×C4—442no—
347C22×C4C23×D1111yescharacteristic
348SD16—28no—
349D8—28no—
350M16—22no—
351M16—222no—
352M16—222no—
353M16—444no—
354M16C22×Dic1114yes—
355C2×C8—22no—
356C2×C8—112no—
357C2×C8—112no—
358C2×C8—222no—
359C2×C8—222no—
360C2×C8—222no—
361C2×C8—444no—
362C4⋊C4—112no—
363C4⋊C4—112no—
364C4⋊C4—222no—
365C4⋊C4—222no—
366C4⋊C4—442no—
367C22⋊C4—44no—
368C22⋊C4—222no—
369C22⋊C4—441no—
370C22⋊C4—441no—
371C22⋊C4—442no—
372C42—21no—
373C42—222no—
374C42—442no—
375C42C22×Dic1112yes—
376C11#2289511yescharacteristic, complemented, Sylow
377C23—22no—
378C23—22no—
379C23—41no—
380C23—41no—
381C23—82no—
382C23#6703711yescharacteristic
383Q8—22no—
384Q8—24no—
385Q8—44no—
386Q8—42no—
387Q8D4×Dic1114yes—
388D4—24no—
389D4—24no—
390D4—24no—
391D4—22no—
392D4—44no—
393D4—42no—
394D4D4×Dic1114yes—
395C2×C4—22no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—48no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—222no—
405C2×C4—222no—
406C2×C4—442no—
407C2×C4—882no—
408C2×C4—1762no—
409C2×C4—1762no—
410C2×C4C2×D4×D1112yes—
411C2×C4C2×#434112yes—
412C2×C4#6703711yescharacteristic
413C2×C4C23×Dic1111yescharacteristic
414C8—24no—
415C8—222no—
416C8—222no—
417C8—442no—
418C22—22no—
419C22—24no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22—82no—
424C22—82no—
425C22—161no—
426C22#1062311811yescharacteristic
427C22#1062312111yescharacteristic
428C22#1062332911yescharacteristic
429C4—24no—
430C4—42no—
431C4—42no—
432C4—442no—
433C4—442no—
434C4—882no—
435C4#1062312212yes—
436C4C2×D4×Dic1112yes—
437C2—21no—
438C2—21no—
439C2—44no—
440C2—82no—
441C2#1307160011yescharacteristic
442C2#1308039512yes—
subgroupG/H
centerC22#10623121
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#454C2
socleC22×C11D42
cosocleC22×C4×C11C24
hypercenterC2×#454D11
hypocenterC11#22895
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#454

Complements

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

NH ≅ G/Ntype
1. #13077449C2semidirect
2. #13077149C2semidirect
3. #13069428C2semidirect
4. #13069273C2semidirect
5. #13069126C2semidirect
6. #13069005C2semidirect
7. #13068851C2semidirect
8. #13068454C2semidirect
16. C11×#454C4semidirect
42. C11×2−1+4C2×C4semidirect
50. C11×AGL(1,ℤ/8)C2×C4semidirect
55. C11×#124C2×C4semidirect
74. C11×#104C2×C4semidirect
75. C11×#101C2×C4semidirect
212. #454Dic11semidirect
257. 2−1+4C2×Dic11semidirect
265. AGL(1,ℤ/8)C2×Dic11semidirect
276. #124C2×Dic11semidirect
291. #104C2×Dic11semidirect
304. #101C2×Dic11semidirect
376. C11#22895semidirect

Maximal subgroups

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

subgroupindex
#130774492
#130771492
#130694282
#130692732
#130691262
#130690052
#130688512
#130684542
C2×C11×#4542
#2289511