Finite Group Databasebeta

← #14774571

Subgroups — #14774571

Order 2816.

1020 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077460C212yesmaximal, complemented
2#13077142C212yesmaximal
3#13069433C211yesmaximal, characteristic, complemented
4#13069280C212yesmaximal, complemented
5#13069133C212yesmaximal, complemented
6#13069020C211yesmaximal, characteristic, complemented
7#13068844C212yesmaximal, complemented
8#13068461C212yesmaximal, complemented
9C2×C11×#455C211yesmaximal, characteristic
10C2×C11×H(5,𝔽2)C2211yescharacteristic
11C2×C11×#137C2212yes—
12C2×C11×#124C2211yescharacteristic
13#10623358C2212yes—
14C2×#67001C2212yes—
15#10623343C2211yescharacteristic, complemented
16C11×#455C418yescomplemented
17C2×C11×#104C2212yes—
18C2×C11×#100C2211yescharacteristic
19#10622846—22no—
20#10622846C2212yes—
21#10622845—22no—
22#10622845C2212yes—
23C2×#66900C2211yescharacteristic, complemented
24C2×#66899C2212yescomplemented
25#10622828—22no—
26#10622828C2212yes—
27C2×#66896—22no—
28C2×#66896C2212yes—
29#10622797—22no—
30Q16×Dic11—22no—
31#10622777—22no—
32SD16×Dic11—22no—
33#10622735C2212yescomplemented
34#10622734C2212yescomplemented
35#10622548C2211yescharacteristic, complemented
36C2×#66867C2211yescharacteristic, complemented
37#10622196C2212yescomplemented
38#10622192C2212yescomplemented
39#10622161C2212yescomplemented
40C11×H(5,𝔽2)—24no—
41C11×H(5,𝔽2)—41no—
42C11×H(5,𝔽2)C2×C414yes—
43C2×C11×#41—22no—
44C2×C11×#41C2312yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11—22no—
47C22×D4×C11—41no—
48C22×D4×C11C2311yescharacteristic
49C11×#137—24no—
50C11×#137C2×C418yescomplemented
51C2×C11×Q16—22no—
52C2×C11×SD16—22no—
53C2×C11×M16C2312yes—
54C11×#124—41no—
55C11×#124C2×C414yescomplemented
56C2×C11×C22⋊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×#100C2×C414yescomplemented
77#66900—41no—
78#66899—22no—
79#66899—22no—
80#66899—22no—
81#66899D412yes—
82#66899D412yes—
83#66896—22no—
84#66896—22no—
85#66896—22no—
86#66896—22no—
87#66896—22no—
88#66896D412yes—
89#66896D412yes—
90#66882—22no—
91#66881—22no—
92#66879—22no—
93C8×Dic11—22no—
94#66867—41no—
95#22890—111nomaximal, Sylow
96C24×C11—21no—
97C24×C11—41no—
98C11×#41—22no—
99C11×#41—22no—
100C11×#41—28no—
101C11×#41—44no—
102C11×#41C22×C414yes—
103C11×#41#4114yes—
104C2×Q8×C11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11C22×C412yes—
108C2×Q8×C11C2×D412yes—
109C2×D4×C11—22no—
110C2×D4×C11—28no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—21no—
114C2×D4×C11—44no—
115C2×D4×C11—42no—
116C2×D4×C11—44no—
117C2×D4×C11—44no—
118C2×D4×C11C22×C412yes—
119C2×D4×C11C2×D412yes—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—41no—
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×C22⋊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×#455D1111yescharacteristic
158#2947—112no—
159#2897—112no—
160#1959—111no—
161#1931—112no—
162#1908—112no—
163#1888—111no—
164#1859—112no—
165#1765—112no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—44no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—81no—
172C23×C11—81no—
173C23×C11—161no—
174C23×C11—161no—
175C23×C11H(5,𝔽2)11yescharacteristic
176Q8×C11—22no—
177Q8×C11—24no—
178Q8×C11—42no—
179Q8×C11C4×D414yes—
180D4×C11—24no—
181D4×C11—24no—
182D4×C11—24no—
183D4×C11—22no—
184D4×C11—48no—
185D4×C11—42no—
186D4×C11C4×D414yes—
187C2×C4×C11—22no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—44no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11C23×C411yescharacteristic
198C2×C4×C11C22×D412yes—
199C2×C4×C11C2×#4112yes—
200C2×C4×C11H(5,𝔽2)11yescharacteristic
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—42no—
204C2×Dic11—82no—
205C2×Dic11—162no—
206C8×C11—24no—
207C11⋊C8—22no—
208C11⋊C8—22no—
209C11⋊C8—42no—
210C2×H(5,𝔽2)C2×D1111yescharacteristic
211C2×#137C2×D1112yes—
212C2×#131—112no—
213C2×#124C2×D1111yescharacteristic
214#520—112no—
215#519—111no—
216#455Dic1118yescomplemented
217#441—222no—
218#440—222no—
219C4×Q16—222no—
220C4×SD16—222no—
221#428—112no—
222C2×#104C2×D1112yes—
223#418—112no—
224#418—222no—
225#417—112no—
226#417—222no—
227#416—112no—
228#416—222no—
229C2×#103—112no—
230C2×#102—112no—
231C2×#102—222no—
232C2×#101—111no—
233C2×#100C2×D1111yescharacteristic
234#405—112no—
235C2×#97—111no—
236#384—111no—
237#343—112no—
238#341—112no—
239#339—112no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—24no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—82no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11—161no—
250C22×C11—164no—
251C22×C11#51811yescharacteristic
252C22×C11D4211yescharacteristic
253C22×C11#55111yescharacteristic
254C4×C11—24no—
255C4×C11—42no—
256C4×C11—42no—
257C4×C11C2×C4×D412yes—
258C4×C11#54612yes—
259Dic11—42no—
260Dic11—42no—
261Dic11—82no—
262H(5,𝔽2)—24no—
263H(5,𝔽2)—41no—
264H(5,𝔽2)C2×Dic1114yes—
265C2×#41—22no—
266C2×#41C22×D1112yes—
267C22×Q8C22×D1111yescharacteristic
268C22×D4—22no—
269C22×D4—41no—
270C22×D4C22×D1111yescharacteristic
271#137—24no—
272#137C2×Dic1118yescomplemented
273C2×Q16—22no—
274C2×SD16—22no—
275#131—224no—
276#131—442no—
277C2×M16—112no—
278C2×M16—222no—
279C2×M16C22×D1112yes—
280C22×C8—112no—
281C22×C8—222no—
282#124—41no—
283#124C2×Dic1114yescomplemented
284C4×Q8—222no—
285C4×Q8—222no—
286C4×Q8—222no—
287C4×D4—222no—
288C4×D4—442no—
289#117—112no—
290#117—222no—
291#117—441no—
292C2×C4⋊C4—112no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—441no—
295C2×C22⋊C4—41no—
296C2×C42C22×D1111yescharacteristic
297#107—222no—
298#106—222no—
299#104C2×Dic1118yescomplemented
300#103—112no—
301#103—112no—
302#103—222no—
303#103—222no—
304#103—222no—
305#102—112no—
306#102—112no—
307#102—222no—
308#102—222no—
309#102—222no—
310#102—222no—
311#102—222no—
312#101—441no—
313#100C2×Dic1114yescomplemented
314#97—222no—
315#97—441no—
316C4×C8—222no—
317C2×C11—21no—
318C2×C11—21no—
319C2×C11—44no—
320C2×C11—82no—
321C2×C11#235811yescharacteristic
322C2×C11#328811yescharacteristic
323C2×C11#328911yescharacteristic
324C24—21no—
325C24—41no—
326#41—22no—
327#41—22no—
328#41—28no—
329#41—44no—
330#41#434114yes—
331#41C22×Dic1114yes—
332C2×Q8—21no—
333C2×Q8—22no—
334C2×Q8—22no—
335C2×Q8D4×D1112yes—
336C2×Q8C22×Dic1112yes—
337C2×D4—22no—
338C2×D4—28no—
339C2×D4—22no—
340C2×D4—22no—
341C2×D4—21no—
342C2×D4—44no—
343C2×D4—42no—
344C2×D4—44no—
345C2×D4—44no—
346C2×D4D4×D1112yes—
347C2×D4C22×Dic1112yes—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—41no—
352C22×C4—222no—
353C22×C4—442no—
354C22×C4C23×D1111yescharacteristic
355Q16—28no—
356SD16—28no—
357M16—22no—
358M16—222no—
359M16—222no—
360M16—444no—
361M16C22×Dic1114yes—
362C2×C8—22no—
363C2×C8—112no—
364C2×C8—112no—
365C2×C8—222no—
366C2×C8—222no—
367C2×C8—222no—
368C2×C8—444no—
369C4⋊C4—112no—
370C4⋊C4—112no—
371C4⋊C4—222no—
372C4⋊C4—222no—
373C4⋊C4—442no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4—882no—
377C22⋊C4—44no—
378C22⋊C4—222no—
379C22⋊C4—442no—
380C42—21no—
381C42—222no—
382C42—442no—
383C42—442no—
384C42C22×Dic1112yes—
385C11#2289011yescharacteristic, complemented, Sylow
386C23—22no—
387C23—22no—
388C23—44no—
389C23—41no—
390C23—41no—
391C23—81no—
392C23—81no—
393C23—161no—
394C23—161no—
395C23#6703711yescharacteristic
396Q8—22no—
397Q8—24no—
398Q8—42no—
399Q8D4×Dic1114yes—
400D4—24no—
401D4—24no—
402D4—24no—
403D4—22no—
404D4—48no—
405D4—42no—
406D4D4×Dic1114yes—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—44no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—222no—
418C2×C4—222no—
419C2×C4—442no—
420C2×C4—882no—
421C2×C4—1762no—
422C2×C4C2×D4×D1112yes—
423C2×C4C2×#434112yes—
424C2×C4#6703711yescharacteristic
425C2×C4C23×Dic1111yescharacteristic
426C8—24no—
427C8—222no—
428C8—222no—
429C8—442no—
430C22—21no—
431C22—21no—
432C22—24no—
433C22—42no—
434C22—42no—
435C22—42no—
436C22—82no—
437C22—81no—
438C22—81no—
439C22—161no—
440C22—164no—
441C22#1062311811yescharacteristic
442C22#1062312111yescharacteristic
443C22#1062332911yescharacteristic
444C4—24no—
445C4—42no—
446C4—42no—
447C4—442no—
448C4—442no—
449C4—882no—
450C4#1062312212yes—
451C4C2×D4×Dic1112yes—
452C2—21no—
453C2—21no—
454C2—44no—
455C2—82no—
456C2#1307160011yescharacteristic
457C2#1308038511yescharacteristic
458C2#1308039411yescharacteristic
subgroupG/H
centerC22#10623121
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#455C2
socleC22×C11D42
prime radicalC2×C11×H(5,𝔽2)C22
cosocleC22×C4×C11C24
hypercenterC2×#455D11
hypocenterC11#22890
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#455

Complements

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

NH ≅ G/Ntype
1. #13077460C2semidirect
3. #13069433C2semidirect
4. #13069280C2semidirect
5. #13069133C2semidirect
6. #13069020C2semidirect
7. #13068844C2semidirect
8. #13068461C2semidirect
15. #10623343C22semidirect
16. C11×#455C4semidirect
23. C2×#66900C22semidirect
24. C2×#66899C22semidirect
33. #10622735C22semidirect
34. #10622734C22semidirect
35. #10622548C22semidirect
36. C2×#66867C22semidirect
37. #10622196C22semidirect
38. #10622192C22semidirect
39. #10622161C22semidirect
50. C11×#137C2×C4semidirect
55. C11×#124C2×C4semidirect
75. C11×#104C2×C4semidirect
76. C11×#100C2×C4semidirect
216. #455Dic11semidirect
272. #137C2×Dic11semidirect
283. #124C2×Dic11semidirect
299. #104C2×Dic11semidirect
313. #100C2×Dic11semidirect
385. C11#22890semidirect

Maximal subgroups

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

subgroupindex
#130774602
#130771422
#130694332
#130692802
#130691332
#130690202
#130688442
#130684612
C2×C11×#4552
#2289011