Finite Group Databasebeta

← #14908255

Subgroups — #14908255

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×M32C211yesmaximal, characteristic, complemented
2#13078193C211yesmaximal, characteristic
3C2×#10622801C211yesmaximal, characteristic, complemented
4#13070726C212yesmaximal, complemented
5#13070721C212yesmaximal, complemented
6#13070709C212yesmaximal, complemented
7#13070704C212yesmaximal, complemented
8#13070404C211yesmaximal, characteristic, complemented
9#13070336C211yesmaximal, characteristic, complemented
10#13070328C211yesmaximal, characteristic, complemented
11C2×C11×#510C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C22×C11×Q16C2211yescharacteristic
14#10623359—21no—
15C2×#66999—21no—
16C22×C8×D11C2211yescharacteristic
17C11×#510—24no—
18C2×C11×Q32C2212yescomplemented
19C2×C11×SD32C2212yescomplemented
20C2×C11×M32C2211yescharacteristic
21#10622846—21no—
22C2×#66899—21no—
23#10622801—21no—
24#10622801—21no—
25#10622801C2211yescharacteristic
26#10622801C2212yes—
27#10622801C2211yescharacteristic
28#10622801C2212yes—
29#10622784—21no—
30#10622784—21no—
31#10622770C2211yescharacteristic
32#10622770C2211yescharacteristic
33#10622719C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66876C2211yescharacteristic
36D11×M32—24no—
37C2×#66862C2212yes—
38C2×C16×D11C2212yes—
39#10622202C2212yescomplemented
40#10622202C2212yescomplemented
41#10622202C2212yescomplemented
42#10622200C2212yescomplemented
43#10622143C2212yescomplemented
44#10622142C2212yescomplemented
45C2×C11×#41—21no—
46C22×Q8×C11—21no—
47C22×C4×D11D411yescharacteristic
48C11×#135—22no—
49C11×#135—22no—
50C2×C11×Q16—22no—
51C2×C11×Q16—21no—
52C2×C11×Q16—22no—
53C2×C11×Q16C2312yes—
54C2×C11×Q16C2311yescharacteristic
55C2×C11×SD16—21no—
56C2×C11×D8C2311yescharacteristic
57C22×C8×C11C2311yescharacteristic
58#66999—21no—
59#66999—21no—
60#66999—22no—
61#66999—22no—
62#66999—41no—
63#66999—41no—
64#66991—21no—
65#66991—21no—
66#66990—41no—
67#66988—41no—
68C4×C22⋊D11—41no—
69C4×C22⋊D11—41no—
70C2×(C2×D11)⋊C4—41no—
71#66979—21no—
72C2×C4⋊Dic11—21no—
73C2×Dic11⋊C4—41no—
74C22×C11⋊C8D411yescharacteristic
75C2×C8×D11—22no—
76C2×C8×D11—22no—
77C2×C8×D11D411yescharacteristic
78C2×C8×D11D411yescharacteristic
79C2×C8×D11C2311yescharacteristic
80C2×C8×D11C2311yescharacteristic
81C11×Q32—24no—
82C11×SD32—24no—
83C11×M32D414yescomplemented
84C2×C11×C16C2312yes—
85#66899—21no—
86#66899—21no—
87#66899—22no—
88#66899—22no—
89#66896—21no—
90#66896—21no—
91#66882—21no—
92#66882C2311yescharacteristic
93#66882C2311yescharacteristic
94#66882C2312yes—
95#66881—21no—
96#66876—22no—
97C2×C11⋊C16C2312yes—
98#66862—24no—
99C16×D11—24no—
100#33606—111nomaximal, Sylow
101C23×D11D811yescharacteristic
102C11×#41—42no—
103C11×#41—42no—
104C2×Q8×C11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11—41no—
107C2×Q8×C11—42no—
108C2×Q8×C11—42no—
109C2×D4×C11—21no—
110C2×D4×C11—41no—
111C22×C4×C11—41no—
112C22×C4×C11—41no—
113C22×C4×C11C2×D411yescharacteristic
114C2×C22⋊D11—41no—
115C2×C22⋊D11—41no—
116C22×Dic11—41no—
117C22×Dic11D811yescharacteristic
118C2×C4×D11—22no—
119C2×C4×D11—22no—
120C2×C4×D11D811yescharacteristic
121C2×C4×D11D811yescharacteristic
122C2×C4×D11C2×D411yescharacteristic
123C2×C4×D11C2×D411yescharacteristic
124C11×Q16—22no—
125C11×Q16—21no—
126C11×Q16—22no—
127C11×Q16—21no—
128C11×Q16—42no—
129C11×SD16—42no—
130C11×D8—21no—
131C11×D8—21no—
132C2×C8×C11C2×D412yes—
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11#4112yes—
135C2×C8×C11C2411yescharacteristic
136C22⋊Dic11—41no—
137C22⋊Dic11—41no—
138C22⋊Dic11—41no—
139(C2×D11)⋊C4—42no—
140(C2×D11)⋊C4—42no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—22no—
146C4⋊Dic11—41no—
147Dic11⋊C4—42no—
148Dic11⋊C4—42no—
149Dic11⋊C4—41no—
150Dic11⋊C4—41no—
151C4×Dic11—41no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8C2×D411yescharacteristic
154C2×C11⋊C8C2×D411yescharacteristic
155C8×D11—22no—
156C8×D11—22no—
157C8×D11—21no—
158C8×D11—21no—
159C8×D11—21no—
160C8×D11—21no—
161C11×C16C2×D414yes—
162C11⋊C16—22no—
163C2×#510D1111yescharacteristic, complemented
164C22×M32—111no—
165#3050—111no—
166C2×#467—111no—
167#2220—112no—
168#2219—112no—
169#2217—112no—
170#2216—112no—
171#2159—111no—
172#2141—111no—
173#2139—111no—
174C23×C11—41no—
175C23×C11C2×D811yescharacteristic
176C22×D11—22no—
177C22×D11—22no—
178C22×D11—41no—
179C22×D11C2×D811yescharacteristic
180C22×D11C2×D811yescharacteristic
181Q8×C11—41no—
182Q8×C11—42no—
183Q8×C11—42no—
184Q8×C11—41no—
185Q8×C11—82no—
186D4×C11—41no—
187D4×C11—41no—
188D4×C11—82no—
189C2×C4×C11—41no—
190C2×C4×C11—42no—
191C2×C4×C11—82no—
192C2×C4×C11—82no—
193C2×C4×C11#12112yes—
194C2×C4×C11C2×D811yescharacteristic
195C2×C4×C11#13512yes—
196C2×C4×C11C22×D411yescharacteristic
197C22⋊D11—82no—
198C22⋊D11—82no—
199C2×Dic11—22no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—42no—
203C2×Dic11—82no—
204C2×Dic11C2×D811yescharacteristic
205C2×Dic11C2×D811yescharacteristic
206C4×D11—21no—
207C4×D11—21no—
208C4×D11—21no—
209C4×D11—21no—
210C4×D11—22no—
211C4×D11—22no—
212C8×C11#12112yes—
213C8×C11C22×D411yescharacteristic
214C8×C11C2×#4111yescharacteristic
215C11⋊C8—21no—
216C11⋊C8—21no—
217C2×#135C2×D1111yescharacteristic
218C22×Q16C2×D1111yescharacteristic
219C23×C8—111no—
220#525—221no—
221C2×C22⋊Q8—221no—
222#510—24no—
223C2×Q32C2×D1112yescomplemented
224C2×SD32C2×D1112yescomplemented
225C2×M32—111no—
226C2×M32—112no—
227C2×M32—224no—
228C2×M32C2×D1111yescharacteristic
229C22×C16—112no—
230#467—111no—
231#467—112no—
232#467—111no—
233#467—112no—
234#467—221no—
235#467—221no—
236#466—111no—
237#466—111no—
238#465—221no—
239#465—221no—
240#427—111no—
241C2×#107—111no—
242#416—221no—
243C2×#103—221no—
244#367—112no—
245#366—112no—
246#358—112no—
247#358—112no—
248#358—112no—
249#357—112no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—81no—
253C22×C11—81no—
254C22×C11—81no—
255C22×C11#46612yes—
256C22×C11C22×D811yescharacteristic
257C2×D11—21no—
258C2×D11—21no—
259C2×D11—21no—
260C2×D11—21no—
261C2×D11—21no—
262C2×D11—44no—
263C2×D11#51012yescomplemented
264C4×C11—81no—
265C4×C11—82no—
266C4×C11#46612yes—
267C4×C11C2×#12111yescharacteristic
268C4×C11C2×#13511yescharacteristic
269Dic11—21no—
270Dic11—21no—
271Dic11—81no—
272Dic11—82no—
273Dic11—81no—
274C2×#41—21no—
275C22×Q8—21no—
276C23×C4—111no—
277#135—22no—
278#135—22no—
279C2×Q16—21no—
280C2×Q16—22no—
281C2×Q16—22no—
282C2×Q16C22×D1112yes—
283C2×Q16C22×D1111yescharacteristic
284C2×SD16—21no—
285C2×D8C22×D1111yescharacteristic
286C22×C8—111no—
287C22×C8—111no—
288C22×C8—111no—
289C22×C8—111no—
290C22×C8—111no—
291C22×C8—222no—
292C22×C8—222no—
293C22×C8C22×D1111yescharacteristic
294#123—441no—
295C22⋊Q8—222no—
296C22⋊Q8—222no—
297C22⋊Q8—221no—
298C22⋊Q8—221no—
299C22⋊Q8—441no—
300C22⋊Q8—441no—
301#121—221no—
302#121—221no—
303#120—441no—
304C4×D4—441no—
305C4×D4—441no—
306#117—221no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—441no—
309C2×C22⋊C4—441no—
310Q32—24no—
311SD32—24no—
312M32—222no—
313M32—224no—
314M32C22⋊D1114yescomplemented
315C2×C16—112no—
316C2×C16—224no—
317C2×C16C22×D1112yes—
318#107—112no—
319#107—111no—
320#107—111no—
321#107—221no—
322#106—221no—
323#103—222no—
324#103—222no—
325#103—221no—
326#103—221no—
327#102—221no—
328#102—221no—
329C2×C11—22no—
330C2×C11—161no—
331C2×C11C2×#46611yescharacteristic
332C2×C11C2×#51011yescharacteristic
333C2×C11#341411yescharacteristic
334D11—22no—
335D11—41no—
336C24—111no—
337#41—42no—
338#41—42no—
339C2×Q8—21no—
340C2×Q8—22no—
341C2×Q8—41no—
342C2×Q8—42no—
343C2×Q8—42no—
344C2×D4—21no—
345C2×D4—41no—
346C2×D4—441no—
347C2×D4—441no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—111no—
351C22×C4—111no—
352C22×C4—111no—
353C22×C4—111no—
354C22×C4—111no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—441no—
358C22×C4D4×D1111yescharacteristic
359Q16—22no—
360Q16—21no—
361Q16—22no—
362Q16—21no—
363Q16—42no—
364SD16—42no—
365D8—21no—
366D8—21no—
367C2×C8—111no—
368C2×C8—111no—
369C2×C8—222no—
370C2×C8—222no—
371C2×C8—222no—
372C2×C8—221no—
373C2×C8—221no—
374C2×C8—221no—
375C2×C8—221no—
376C2×C8D4×D1111yescharacteristic
377C2×C8#434112yes—
378C2×C8C2×C22⋊D1112yes—
379C2×C8C23×D1111yescharacteristic
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—222no—
383C4⋊C4—442no—
384C4⋊C4—442no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C22⋊C4—442no—
389C22⋊C4—442no—
390C22⋊C4—441no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C22⋊C4—441no—
395C42—441no—
396C16—222no—
397C16C2×C22⋊D1114yes—
398C11#3360611yescharacteristic, complemented, Sylow
399C23—41no—
400C23—111no—
401C23—111no—
402C23—222no—
403C23—222no—
404C23—441no—
405C23D8×D1111yescharacteristic
406Q8—42no—
407Q8—41no—
408Q8—41no—
409Q8—42no—
410Q8—82no—
411D4—41no—
412D4—41no—
413D4—82no—
414D4—882no—
415D4—882no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—111no—
421C2×C4—111no—
422C2×C4—222no—
423C2×C4—222no—
424C2×C4—222no—
425C2×C4—221no—
426C2×C4—221no—
427C2×C4—221no—
428C2×C4—221no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—442no—
432C2×C4—882no—
433C2×C4D8×D1111yescharacteristic
434C2×C4#6696512yes—
435C2×C4#6699112yes—
436C2×C4C2×D4×D1111yescharacteristic
437C8—221no—
438C8—221no—
439C8#6699112yes—
440C8C2×#434111yescharacteristic
441C8C22×C22⋊D1111yescharacteristic
442C22—21no—
443C22—21no—
444C22—81no—
445C22—81no—
446C22—81no—
447C22—112no—
448C22—221no—
449C22—221no—
450C22—221no—
451C22—221no—
452C22—221no—
453C22—444no—
454C22#1062277012yes—
455C22C2×D8×D1111yescharacteristic
456C4—81no—
457C4—82no—
458C4—221no—
459C4—221no—
460C4—881no—
461C4—882no—
462C4—881no—
463C4#1062277012yes—
464C4C2×#6696511yescharacteristic
465C4C2×#6699111yescharacteristic
466C2—22no—
467C2—161no—
468C2—222no—
469C2—441no—
470C2C2×#1062277011yescharacteristic
471C2D11×#51011yescharacteristic
472C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#510C2
socleC22×C11C22×D8
prime radical#13078193C2
hypercenterC2×#510D11
hypocenterC11#33606
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

Complements

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

NH ≅ G/Ntype
1. C2×D11×M32C2semidirect
3. C2×#10622801C2semidirect
4. #13070726C2semidirect
5. #13070721C2semidirect
6. #13070709C2semidirect
7. #13070704C2semidirect
8. #13070404C2semidirect
9. #13070336C2semidirect
10. #13070328C2semidirect
11. C2×C11×#510C2semidirect
18. C2×C11×Q32C22semidirect
19. C2×C11×SD32C22semidirect
39. #10622202C22semidirect
40. #10622202C22semidirect
41. #10622202C22semidirect
42. #10622200C22semidirect
43. #10622143C22semidirect
44. #10622142C22semidirect
83. C11×M32D4semidirect
163. C2×#510D11semidirect
223. C2×Q32C2×D11semidirect
224. C2×SD32C2×D11semidirect
263. C2×D11#510semidirect
314. M32C22⋊D11semidirect
398. C11#33606semidirect

Maximal subgroups

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

subgroupindex
C2×D11×M322
#130781932
C2×#106228012
#130707262
#130707212
#130707092
#130707042
#130704042
#130703362
#130703282
C2×C11×#5102
#3360611