Finite Group Databasebeta

← #14908606

Subgroups — #14908606

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#467C211yesmaximal, characteristic
2D11×#427C211yesmaximal, characteristic
3#13070825C211yesmaximal, characteristic, complemented
4#13070824C211yesmaximal, characteristic, complemented
5#13070821C211yesmaximal, characteristic, complemented
6#13070820C211yesmaximal, characteristic, complemented
7#13070817C211yesmaximal, characteristic, complemented
8#13070815C211yesmaximal, characteristic, complemented
9#13070812C211yesmaximal, characteristic, complemented
10#13070403C211yesmaximal, characteristic, complemented
11#13070401C211yesmaximal, characteristic, complemented
12#13070334C211yesmaximal, characteristic, complemented
13#13070334C211yesmaximal, characteristic, complemented
14#13070225C211yesmaximal, characteristic
15C11×#2237C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18D11×C22⋊Q8—21no—
19D11×#117—21no—
20C11×#467C2211yescharacteristic
21C11×#427C2211yescharacteristic
22#10622801C2211yescharacteristic
23#10622729C2211yescharacteristic
24#10622719C2211yescharacteristic
25#10622664—21no—
26#10622611—21no—
27C2×#66862C2211yescharacteristic
28C2×#66862C2211yescharacteristic
29#10622500C2211yescharacteristic
30#10622493C2211yescharacteristic
31#10622493C2211yescharacteristic
32D11×#107C2211yescharacteristic
33D11×#107C2211yescharacteristic
34D11×#107C2211yescharacteristic
35#10622473—21no—
36D11×#106—21no—
37#10622426—21no—
38D11×#103—21no—
39C11×#367C2211yescharacteristic, complemented
40C11×#366C2211yescharacteristic, complemented
41C11×#358C2211yescharacteristic, complemented
42C11×#358C2211yescharacteristic, complemented
43C11×C22⋊C16C2211yescharacteristic
44#10622202C2211yescharacteristic, complemented
45#10622202C2211yescharacteristic, complemented
46C22⋊(C11⋊C16)C2211yescharacteristic
47(C2×D11)⋊C16C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622143C2211yescharacteristic, complemented
50#10622142C2211yescharacteristic, complemented
51#10622141C2211yescharacteristic, complemented
52#10622141C2211yescharacteristic, complemented
53#10622130C2211yescharacteristic, complemented
54#10622130C2211yescharacteristic, complemented
55#10622128C2211yescharacteristic, complemented
56#10622128C2211yescharacteristic, complemented
57#10622127C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×Q8×D11—21no—
60C22×C4×D11D411yescharacteristic
61C2×C11×Q16C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×C22⋊Q8—21no—
64C11×#117—21no—
65#66999—21no—
66C2×#4326—21no—
67#66979—21no—
68#66977—21no—
69C22×C11⋊C8D411yescharacteristic
70Q16×D11—22no—
71Q16×D11—22no—
72C2×Dic44C2311yescharacteristic
73C2×C8×D11—22no—
74C2×C8×D11—22no—
75C2×C8×D11D411yescharacteristic
76C2×C8×D11D411yescharacteristic
77C2×C8×D11C2311yescharacteristic
78C2×C8×D11C2311yescharacteristic
79#66950—21no—
80#66949—41no—
81#66945—21no—
82#66945—21no—
83C4⋊C4×D11—21no—
84C4⋊C4×D11—21no—
85C4⋊C4×D11—21no—
86C4⋊C4×D11—41no—
87C22⋊C4×D11—41no—
88C22⋊C4×D11—41no—
89#66931—41no—
90#66930—41no—
91#66925—41no—
92C42×D11—41no—
93C2×C11×C16C2311yescharacteristic
94C2×C11×C16C2311yescharacteristic
95C11×#107C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#106—21no—
99C11×#103—21no—
100#66899—21no—
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66881—21no—
105#66880—21no—
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66874—21no—
109#66872—21no—
110#66872—21no—
111#66871—21no—
112#66871—21no—
113#66871—21no—
114#66862—22no—
115#66862—22no—
116#33649—111nomaximal, Sylow
117C23×D11D811yescharacteristic
118C2×Q8×C11—21no—
119C22×C4×C11C2×D411yescharacteristic
120C22×Dic11D811yescharacteristic
121Q8×D11—42no—
122Q8×D11—42no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—41no—
126C2×C4×D11—41no—
127C2×C4×D11—41no—
128C2×C4×D11—41no—
129C2×C4×D11D811yescharacteristic
130C2×C4×D11D811yescharacteristic
131C2×C4×D11C2×D411yescharacteristic
132C2×C4×D11C2×D411yescharacteristic
133C2×Dic22—21no—
134C2×Dic22—41no—
135C11×Q16—21no—
136C11×Q16—21no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11C2411yescharacteristic
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—41no—
145C11×C22⋊C4—41no—
146C11×C22⋊C4—41no—
147C42×C11—41no—
148C22⋊Dic11—41no—
149C22⋊Dic11—41no—
150#4326—42no—
151(C2×D11)⋊C4—41no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163Dic11⋊C4—41no—
164C4×Dic11—41no—
165C4×Dic11—41no—
166C4×Dic11—41no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8C2×D411yescharacteristic
169C2×C11⋊C8C2×D411yescharacteristic
170Dic44—21no—
171Dic44—21no—
172C8×D11—22no—
173C8×D11—21no—
174C8×D11—21no—
175C8×D11—22no—
176C8×D11#4112yes—
177C8×D11#4112yes—
178C11×C16—21no—
179C11×C16—21no—
180C11⋊C16—21no—
181C11⋊C16—21no—
182C2×#467—111no—
183C2×#427—111no—
184#2237—111no—
185#2237—111no—
186#2237—111no—
187#2237D1111yescharacteristic, complemented
188#2236—111no—
189#2236—111no—
190#2235—111no—
191#2235—111no—
192#2159—111no—
193#2159—111no—
194#2141—111no—
195#2141—111no—
196#2112—111no—
197C23×C11C2×D811yescharacteristic
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—41no—
201C22×D11C2×D811yescharacteristic
202C22×D11C2×D811yescharacteristic
203Q8×C11—41no—
204Q8×C11—41no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×Dic11—22no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11C2×D811yescharacteristic
219C2×Dic11C2×D811yescharacteristic
220C4×D11—22no—
221C4×D11—21no—
222C4×D11—21no—
223C4×D11—22no—
224C4×D11—82no—
225C4×D11—82no—
226C4×D11—82no—
227C4×D11—82no—
228C4×D11#12312yes—
229C4×D11#13712yes—
230Dic22—41no—
231Dic22—41no—
232Dic22—82no—
233C8×C11—21no—
234C8×C11C2×#4111yescharacteristic
235C8×C11C2×#4111yescharacteristic
236C11⋊C8—21no—
237C11⋊C8#12312yes—
238C22×Q16—111no—
239C23×C8—111no—
240C2×C22⋊Q8—221no—
241C2×#117—221no—
242C2×M32—111no—
243C2×M32—111no—
244#467—111no—
245#467—111no—
246#467—111no—
247#467—221no—
248#467—221no—
249#467C2×D1111yescharacteristic
250#427—111no—
251#427—111no—
252#427—111no—
253#427—221no—
254#427—221no—
255#427C2×D1111yescharacteristic
256C2×#107—111no—
257C2×#107—111no—
258C2×#107—111no—
259C2×#106—221no—
260C2×#103—221no—
261#367—111no—
262#367—111no—
263#367—111no—
264#367C2×D1111yescharacteristic, complemented
265#366—111no—
266#366—111no—
267#366—111no—
268#366C2×D1111yescharacteristic, complemented
269#358—111no—
270#358—111no—
271#358—111no—
272#358—111no—
273#358—111no—
274#358—111no—
275#358C2×D1111yescharacteristic, complemented
276#358C2×D1111yescharacteristic, complemented
277C22⋊C16—111no—
278C22⋊C16—111no—
279C22⋊C16—111no—
280C22⋊C16C2×D1111yescharacteristic
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11C22×D811yescharacteristic
285C2×D11—21no—
286C2×D11—21no—
287C2×D11—21no—
288C2×D11—21no—
289C2×D11—44no—
290C2×D11#48012yes—
291C2×D11#51012yes—
292C4×C11—21no—
293C4×C11—81no—
294C4×C11—81no—
295C4×C11—81no—
296C4×C11—81no—
297C4×C11C2×#12311yescharacteristic
298C4×C11C2×#13711yescharacteristic
299Dic11—21no—
300Dic11—81no—
301Dic11—81no—
302Dic11—81no—
303Dic11—81no—
304Dic11#48012yes—
305C22×Q8—221no—
306C23×C4—111no—
307C2×Q16—111no—
308C2×Q16—222no—
309C2×Q16—222no—
310C2×Q16—221no—
311C2×Q16C22×D1111yescharacteristic
312C22×C8—111no—
313C22×C8—111no—
314C22×C8—111no—
315C22×C8—111no—
316C22×C8—111no—
317C22×C8—222no—
318C22×C8—222no—
319C22×C8C22×D1111yescharacteristic
320C22⋊Q8—21no—
321C22⋊Q8—221no—
322C22⋊Q8—221no—
323C22⋊Q8—221no—
324C22⋊Q8—441no—
325C22⋊Q8—441no—
326#117—21no—
327#117—221no—
328#117—221no—
329#117—221no—
330#117—441no—
331#117—441no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—441no—
336C2×C22⋊C4—441no—
337C2×C22⋊C4—441no—
338C2×C42—441no—
339M32—222no—
340M32—222no—
341C2×C16—111no—
342C2×C16—111no—
343C2×C16C22×D1111yescharacteristic
344C2×C16C22×D1111yescharacteristic
345#107—111no—
346#107—111no—
347#107—111no—
348#107—221no—
349#107—221no—
350#107—221no—
351#107C22×D1111yescharacteristic
352#107C22×D1111yescharacteristic
353#107C22×D1111yescharacteristic
354#106—21no—
355#106—221no—
356#106—221no—
357#106—221no—
358#103—21no—
359#103—221no—
360#103—221no—
361#103—221no—
362C2×C11—41no—
363C2×C11C2×#48011yescharacteristic
364C2×C11C2×#51011yescharacteristic
365C2×C11#341411yescharacteristic
366D11—22no—
367D11—22no—
368C24—111no—
369C2×Q8—21no—
370C2×Q8—221no—
371C2×Q8—441no—
372C2×Q8—442no—
373C2×Q8—442no—
374C22×C4—111no—
375C22×C4—111no—
376C22×C4—111no—
377C22×C4—111no—
378C22×C4—111no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4—441no—
385C22×C4D4×D1111yescharacteristic
386Q16—21no—
387Q16—21no—
388Q16—221no—
389Q16—221no—
390Q16—442no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—111no—
394C2×C8—112no—
395C2×C8—112no—
396C2×C8—111no—
397C2×C8—222no—
398C2×C8—222no—
399C2×C8—222no—
400C2×C8—221no—
401C2×C8—221no—
402C2×C8D4×D1111yescharacteristic
403C2×C8C23×D1111yescharacteristic
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—41no—
408C4⋊C4—221no—
409C4⋊C4—221no—
410C4⋊C4—221no—
411C4⋊C4—441no—
412C4⋊C4—441no—
413C4⋊C4—441no—
414C4⋊C4—441no—
415C4⋊C4—441no—
416C4⋊C4—441no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—441no—
420C22⋊C4—441no—
421C22⋊C4—441no—
422C22⋊C4—441no—
423C22⋊C4—441no—
424C22⋊C4—441no—
425C42—41no—
426C42—441no—
427C42—441no—
428C42—441no—
429C16—21no—
430C16—21no—
431C16—221no—
432C16—221no—
433C11#3364911yescharacteristic, complemented, Sylow
434C23—111no—
435C23—111no—
436C23—222no—
437C23—222no—
438C23—441no—
439C23D8×D1111yescharacteristic
440Q8—41no—
441Q8—41no—
442Q8—441no—
443Q8—441no—
444Q8—882no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—111no—
452C2×C4—112no—
453C2×C4—112no—
454C2×C4—111no—
455C2×C4—222no—
456C2×C4—222no—
457C2×C4—222no—
458C2×C4—221no—
459C2×C4—221no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—882no—
465C2×C4—882no—
466C2×C4—882no—
467C2×C4—882no—
468C2×C4D8×D1111yescharacteristic
469C2×C4C2×D4×D1111yescharacteristic
470C8—21no—
471C8—112no—
472C8—221no—
473C8#41×D1111yescharacteristic
474C8#41×D1111yescharacteristic
475C22—21no—
476C22—21no—
477C22—21no—
478C22—112no—
479C22—112no—
480C22—221no—
481C22—221no—
482C22—221no—
483C22—221no—
484C22—444no—
485C22C2×D8×D1111yescharacteristic
486C4—21no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—81no—
491C4—112no—
492C4—221no—
493C4—881no—
494C4—881no—
495C4—881no—
496C4—881no—
497C4D11×#12311yescharacteristic
498C4D11×#13711yescharacteristic
499C2—41no—
500C2—222no—
501C2—222no—
502C2D11×#48011yescharacteristic
503C2D11×#51011yescharacteristic
504C2#1308174911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2237C2
socleC22×C11C22×D8
prime radicalC23×D11D8
hypercenter#2237D11
hypocenterC11#33649
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2237

Complements

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

NH ≅ G/Ntype
3. #13070825C2semidirect
4. #13070824C2semidirect
5. #13070821C2semidirect
6. #13070820C2semidirect
7. #13070817C2semidirect
8. #13070815C2semidirect
9. #13070812C2semidirect
10. #13070403C2semidirect
11. #13070401C2semidirect
12. #13070334C2semidirect
13. #13070334C2semidirect
15. C11×#2237C2semidirect
39. C11×#367C22semidirect
40. C11×#366C22semidirect
41. C11×#358C22semidirect
42. C11×#358C22semidirect
44. #10622202C22semidirect
45. #10622202C22semidirect
49. #10622143C22semidirect
50. #10622142C22semidirect
51. #10622141C22semidirect
52. #10622141C22semidirect
53. #10622130C22semidirect
54. #10622130C22semidirect
55. #10622128C22semidirect
56. #10622128C22semidirect
57. #10622127C22semidirect
58. #10622127C22semidirect
187. #2237D11semidirect
264. #367C2×D11semidirect
268. #366C2×D11semidirect
275. #358C2×D11semidirect
276. #358C2×D11semidirect
433. C11#33649semidirect

Maximal subgroups

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

subgroupindex
D11×#4672
D11×#4272
#130708252
#130708242
#130708212
#130708202
#130708172
#130708152
#130708122
#130704032
#130704012
#130703342
#130702252
C11×#22372
#3364911