Finite Group Databasebeta

← #14774598

Subgroups — #14774598

Order 2816.

1012 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077449C212yesmaximal, complemented
2#13077149C212yesmaximal, complemented
3#13069433C211yesmaximal, characteristic, complemented
4#13069273C212yesmaximal, complemented
5#13069126C212yesmaximal, complemented
6#13069005C211yesmaximal, characteristic, complemented
7#13068844C212yesmaximal, complemented
8#13068461C212yesmaximal, 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#10622548C2211yescharacteristic
36C2×#66867C2211yescharacteristic
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⋊Dic11—41no—
70C2×C4⋊Dic11C2312yes—
71C2×#4318—22no—
72C2×#4318C2312yes—
73C22×C11⋊C8—22no—
74C22×C11⋊C8C2312yes—
75C11×#104C2×C418yescomplemented
76C11×#101C2×C414yescomplemented
77#66899—22no—
78#66899—22no—
79#66899—22no—
80#66899—22no—
81#66899—22no—
82#66899D412yes—
83#66899D412yes—
84#66897—41no—
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#22893—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—41no—
128C22×Dic11—41no—
129C11×SD16—28no—
130C11×D8—28no—
131C11×M16—22no—
132C11×M16C22×C414yes—
133C2×C8×C11—22no—
134C11×C22⋊C4—44no—
135C42×C11—21no—
136C42×C11C22×C412yes—
137C22⋊Dic11—22no—
138C22⋊Dic11—42no—
139C22⋊Dic11—42no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—42no—
143C4⋊Dic11—82no—
144C4⋊Dic11C2×D412yes—
145C4⋊Dic11C2×D412yes—
146C4×Dic11—22no—
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×#454D1111yescharacteristic
158#2946—112no—
159#2898—112no—
160#1959—111no—
161#1930—112no—
162#1907—112no—
163#1885—111no—
164#1859—112no—
165#1765—112no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—81no—
171C23×C11—81no—
172C23×C11H(5,𝔽2)11yescharacteristic
173Q8×C11—22no—
174Q8×C11—24no—
175Q8×C11—44no—
176Q8×C11—42no—
177Q8×C11C4×D414yes—
178D4×C11—24no—
179D4×C11—24no—
180D4×C11—24no—
181D4×C11—22no—
182D4×C11—44no—
183D4×C11—42no—
184D4×C11C4×D414yes—
185C2×C4×C11—22no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—48no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11C23×C411yescharacteristic
196C2×C4×C11C22×D412yes—
197C2×C4×C11C2×#4112yes—
198C2×C4×C11H(5,𝔽2)11yescharacteristic
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—42no—
202C2×Dic11—82no—
203C2×Dic11—161no—
204C2×Dic11—161no—
205C2×Dic11—162no—
206C8×C11—24no—
207C11⋊C8—22no—
208C11⋊C8—22no—
209C11⋊C8—42no—
210C2×2−1+4C2×D1111yescharacteristic
211C2×AGL(1,ℤ/8)C2×D1112yes—
212C2×#131—112no—
213C2×#124C2×D1111yescharacteristic
214#520—112no—
215#518—111no—
216#454Dic1118yescomplemented
217#442—222no—
218#440—222no—
219C4×SD16—222no—
220C4×D8—222no—
221#428—112no—
222C2×#104C2×D1112yes—
223#419—112no—
224#419—222no—
225#417—112no—
226#417—222no—
227#416—112no—
228#416—222no—
229C2×#103—112no—
230C2×#103—222no—
231C2×#102—112no—
232C2×#101C2×D1111yescharacteristic
233C2×#100—111no—
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#51811yescharacteristic
251C22×C11D4211yescharacteristic
252C22×C11#55111yescharacteristic
253C4×C11—24no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11C2×C4×D412yes—
257C4×C11#54612yes—
258Dic11—42no—
259Dic11—42no—
260Dic11—82no—
2612−1+4—24no—
2622−1+4—41no—
2632−1+4C2×Dic1114yescomplemented
264C2×#41—22no—
265C2×#41—41no—
266C2×#41C22×D1112yes—
267C22×Q8—22no—
268C22×Q8C22×D1111yescharacteristic
269C22×D4C22×D1111yescharacteristic
270AGL(1,ℤ/8)—24no—
271AGL(1,ℤ/8)C2×Dic1118yescomplemented
272C2×SD16—22no—
273C2×D8—22no—
274#131—224no—
275#131—442no—
276C2×M16—112no—
277C2×M16—222no—
278C2×M16C22×D1112yes—
279C22×C8—112no—
280C22×C8—222no—
281#124—41no—
282#124C2×Dic1114yescomplemented
283C4×Q8—222no—
284C4×D4—222no—
285C4×D4—222no—
286C4×D4—222no—
287C4×D4—442no—
288#117—112no—
289#117—222no—
290C2×C4⋊C4—112no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4—441no—
293C2×C22⋊C4—41no—
294C2×C22⋊C4—441no—
295C2×C42C22×D1111yescharacteristic
296#107—222no—
297#106—222no—
298#104C2×Dic1118yescomplemented
299#103—112no—
300#103—112no—
301#103—222no—
302#103—222no—
303#103—222no—
304#103—222no—
305#103—222no—
306#102—112no—
307#102—112no—
308#102—222no—
309#102—222no—
310#102—222no—
311#101C2×Dic1114yescomplemented
312#100—441no—
313#97—222no—
314#97—441no—
315C4×C8—222no—
316C2×C11—21no—
317C2×C11—21no—
318C2×C11—44no—
319C2×C11—82no—
320C2×C11#235811yescharacteristic
321C2×C11#328811yescharacteristic
322C2×C11#328911yescharacteristic
323C24—21no—
324#41—22no—
325#41—22no—
326#41—28no—
327#41—44no—
328#41—44no—
329#41—44no—
330#41#434114yes—
331#41C22×Dic1114yes—
332C2×Q8—21no—
333C2×Q8—28no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—41no—
337C2×Q8—44no—
338C2×Q8D4×D1112yes—
339C2×Q8C22×Dic1112yes—
340C2×D4—22no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—21no—
344C2×D4—41no—
345C2×D4D4×D1112yes—
346C2×D4C22×Dic1112yes—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—42no—
351C22×C4—222no—
352C22×C4—441no—
353C22×C4—441no—
354C22×C4—442no—
355C22×C4C23×D1111yescharacteristic
356SD16—28no—
357D8—28no—
358M16—22no—
359M16—222no—
360M16—222no—
361M16—444no—
362M16C22×Dic1114yes—
363C2×C8—22no—
364C2×C8—112no—
365C2×C8—112no—
366C2×C8—222no—
367C2×C8—222no—
368C2×C8—222no—
369C2×C8—444no—
370C4⋊C4—112no—
371C4⋊C4—112no—
372C4⋊C4—222no—
373C4⋊C4—222no—
374C4⋊C4—442no—
375C4⋊C4—882no—
376C22⋊C4—44no—
377C22⋊C4—222no—
378C22⋊C4—442no—
379C22⋊C4—442no—
380C42—21no—
381C42—222no—
382C42—442no—
383C42C22×Dic1112yes—
384C11#2289311yescharacteristic, complemented, Sylow
385C23—22no—
386C23—22no—
387C23—41no—
388C23—41no—
389C23—81no—
390C23—81no—
391C23#6703711yescharacteristic
392Q8—22no—
393Q8—24no—
394Q8—44no—
395Q8—42no—
396Q8D4×Dic1114yes—
397D4—24no—
398D4—24no—
399D4—24no—
400D4—22no—
401D4—44no—
402D4—42no—
403D4D4×Dic1114yes—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—48no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—442no—
417C2×C4—882no—
418C2×C4—1761no—
419C2×C4—1761no—
420C2×C4—1762no—
421C2×C4C2×D4×D1112yes—
422C2×C4C2×#434112yes—
423C2×C4#6703711yescharacteristic
424C2×C4C23×Dic1111yescharacteristic
425C8—24no—
426C8—222no—
427C8—222no—
428C8—442no—
429C22—21no—
430C22—21no—
431C22—24no—
432C22—42no—
433C22—42no—
434C22—42no—
435C22—82no—
436C22—81no—
437C22—81no—
438C22—161no—
439C22#1062311811yescharacteristic
440C22#1062312111yescharacteristic
441C22#1062332911yescharacteristic
442C4—24no—
443C4—42no—
444C4—42no—
445C4—442no—
446C4—442no—
447C4—882no—
448C4#1062312212yes—
449C4C2×D4×Dic1112yes—
450C2—21no—
451C2—21no—
452C2—44no—
453C2—82no—
454C2#1307160011yescharacteristic
455C2#1308038411yescharacteristic
456C2#1308039311yescharacteristic
subgroupG/H
centerC22#10623121
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#454C2
socleC22×C11D42
cosocleC22×C4×C11C24
hypercenterC2×#454D11
hypocenterC11#22893
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. #13069433C2semidirect
4. #13069273C2semidirect
5. #13069126C2semidirect
6. #13069005C2semidirect
7. #13068844C2semidirect
8. #13068461C2semidirect
16. C11×#454C4semidirect
42. C11×2−1+4C2×C4semidirect
50. C11×AGL(1,ℤ/8)C2×C4semidirect
55. C11×#124C2×C4semidirect
75. C11×#104C2×C4semidirect
76. C11×#101C2×C4semidirect
216. #454Dic11semidirect
263. 2−1+4C2×Dic11semidirect
271. AGL(1,ℤ/8)C2×Dic11semidirect
282. #124C2×Dic11semidirect
298. #104C2×Dic11semidirect
311. #101C2×Dic11semidirect
384. C11#22893semidirect

Maximal subgroups

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

subgroupindex
#130774492
#130771492
#130694332
#130692732
#130691262
#130690052
#130688442
#130684612
C2×C11×#4542
#2289311