Finite Group Databasebeta

← #14909849

Subgroups — #14909849

Order 2816.

606 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079256C211yesmaximal, characteristic, complemented
2#13079097C211yesmaximal, characteristic, complemented
3#13070881C211yesmaximal, characteristic, complemented
4#13070876C211yesmaximal, characteristic, complemented
5#13070851C211yesmaximal, characteristic, complemented
6#13070838C211yesmaximal, characteristic, complemented
7#13070676C211yesmaximal, characteristic, complemented
8#13070670C211yesmaximal, characteristic, complemented
9#13070654C211yesmaximal, characteristic, complemented
10#13070650C211yesmaximal, characteristic, complemented
11#13070554C211yesmaximal, characteristic, complemented
12#13070541C211yesmaximal, characteristic, complemented
13#13070528C211yesmaximal, characteristic, complemented
14#13070420C211yesmaximal, characteristic, complemented
15C11×#2187C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17#10623336—21no—
18C2×#66985—21no—
19C2×#66957C2211yescharacteristic
20#10623174—21no—
21C2×C11×SD32C2211yescharacteristic
22C2×C11×SD32C2211yescharacteristic
23C11×#467C2211yescharacteristic
24#10622804C2211yescharacteristic, complemented
25Q16×Dic11C2211yescharacteristic, complemented
26C2×#66893C2211yescharacteristic, complemented
27C2×#66892C2211yescharacteristic, complemented
28#10622768C2211yescharacteristic
29#10622768C2211yescharacteristic
30#10622767—21no—
31#10622767—21no—
32#10622764C2211yescharacteristic
33#10622764C2211yescharacteristic
34C2×#66890C2211yescharacteristic
35C2×#66890C2211yescharacteristic
36#10622728C2211yescharacteristic
37#10622714C2211yescharacteristic
38#10622662—21no—
39C2×#66864C2211yescharacteristic, complemented
40C2×D176C2211yescharacteristic, complemented
41#10622487C2211yescharacteristic, complemented
42#10622485C2211yescharacteristic, complemented
43#10622430—21no—
44#10622408—21no—
45C11×#357C2211yescharacteristic
46C11×#357C2211yescharacteristic
47C11×C22⋊C16C2211yescharacteristic
48#10622200C2211yescharacteristic
49#10622200C2211yescharacteristic
50C22⋊(C11⋊C16)C2211yescharacteristic
51#10622147C2211yescharacteristic, complemented
52#10622141C2211yescharacteristic, complemented
53#10622140C2211yescharacteristic, complemented
54Dic11⋊C16C2211yescharacteristic, complemented
55Dic11⋊C16C2211yescharacteristic, complemented
56C16×Dic11C2211yescharacteristic, complemented
57#10622130C2211yescharacteristic, complemented
58#10622129C2211yescharacteristic, complemented
59C22×D4×C11—21no—
60C2×#4339—21no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×D8—21no—
63C2×C11×D8—41no—
64C2×C11×D8—41no—
65C2×C11×D8C2311yescharacteristic
66C2×C11×D8C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C22⋊Q8—21no—
69#67006—41no—
70#67006—41no—
71#67000—21no—
72Q8×Dic11—21no—
73C2×#4325—21no—
74#66993—21no—
75#66993—21no—
76#66991—41no—
77#66991—41no—
78#66989—21no—
79#66989—21no—
80C2×#4324—21no—
81C2×#4324—21no—
82#66985—44no—
83C2×#4323—21no—
84C2×#4323—21no—
85#66983—21no—
86#66979D411yescharacteristic
87C2×#4318D411yescharacteristic
88C2×Dic44C2311yescharacteristic
89#66957—41no—
90#66957—41no—
91C2×D88C2311yescharacteristic
92C2×D88C2311yescharacteristic
93C2×#4314—21no—
94#66951—41no—
95#66950—41no—
96#66946—21no—
97#66941—21no—
98#66938—41no—
99#66936—41no—
100C11×SD32—41no—
101C11×SD32—41no—
102C2×C11×C16C2311yescharacteristic
103C2×C11×C16C2311yescharacteristic
104C11×#107C2311yescharacteristic
105C11×#103—21no—
106#66899—21no—
107#66893—41no—
108#66892—41no—
109#66890—41no—
110#66890—41no—
111#66885—21no—
112#66882C2311yescharacteristic
113#66879D411yescharacteristic
114#66879D411yescharacteristic
115C8×Dic11C2311yescharacteristic
116C8×Dic11C2311yescharacteristic
117C2×C11⋊C16C2311yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119#66873—21no—
120#66871—21no—
121#66864—41no—
122D176—41no—
123#33790—111nomaximal, Sylow
124C24×C11—41no—
125C2×Q8×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11—41no—
131C22×C4×C11C2×D411yescharacteristic
132C2×C22⋊D11—41no—
133C2×C22⋊D11—41no—
134C2×C22⋊D11—41no—
135C2×C22⋊D11—41no—
136C2×C22⋊D11—41no—
137C2×C22⋊D11—41no—
138#4339—42no—
139#4339—42no—
140C2×D44—21no—
141C2×D44—21no—
142C2×C4×D11—41no—
143C2×C4×D11—41no—
144C2×Dic22—21no—
145C2×Dic22—41no—
146C11×Q16—21no—
147C11×Q16—21no—
148C11×D8—21no—
149C11×D8—21no—
150C11×D8—21no—
151C11×D8—21no—
152C11×D8—42no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11C2×D411yescharacteristic
156C2×C8×C11C2411yescharacteristic
157C11×C4⋊C4—21no—
158C11×C4⋊C4—41no—
159C11×C22⋊C4—41no—
160C22⋊Dic11—41no—
161C22⋊Dic11—41no—
162C22⋊Dic11—41no—
163C22⋊Dic11—41no—
164C22⋊Dic11D811yescharacteristic
165C22⋊Dic11D811yescharacteristic
166#4325—42no—
167#4324—42no—
168#4324—42no—
169#4323—42no—
170#4323—42no—
171(C2×D11)⋊C4—41no—
172(C2×D11)⋊C4—41no—
173(C2×D11)⋊C4—41no—
174(C2×D11)⋊C4—41no—
175C4⋊Dic11—21no—
176C4⋊Dic11—41no—
177C4⋊Dic11D811yescharacteristic
178C4⋊Dic11D811yescharacteristic
179Dic11⋊C4—41no—
180C4×Dic11—41no—
181C4×Dic11C2×D411yescharacteristic
182C4×Dic11C2×D411yescharacteristic
183#4318—22no—
184C2×C11⋊C8C2×D411yescharacteristic
185C2×C11⋊C8C2×D411yescharacteristic
186Dic44—21no—
187Dic44—21no—
188D88—21no—
189D88—21no—
190D88—21no—
191D88—21no—
192#4314—42no—
193C11×C16—21no—
194C11×C16—21no—
195C11⋊C16—21no—
196C11⋊C16—21no—
197#3175—111no—
198#3155—111no—
199#2250—111no—
200#2249—111no—
201#2243—111no—
202#2240—111no—
203#2211—111no—
204#2210—111no—
205#2207—111no—
206#2206—111no—
207#2189—111no—
208#2187D1111yescharacteristic, complemented
209#2186—111no—
210#2184—111no—
211#2164—111no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—82no—
215C23×C11—161no—
216C23×C11—161no—
217C23×C11C2×D811yescharacteristic
218C22×D11—41no—
219C22×D11—41no—
220Q8×C11—41no—
221Q8×C11—41no—
222D4×C11—41no—
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—41no—
226D4×C11—82no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11C2×D811yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C22⋊D11—82no—
234C22⋊D11—161no—
235C22⋊D11—161no—
236C22⋊D11—161no—
237C22⋊D11—161no—
238C22⋊D11—161no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11C2×D811yescharacteristic
242C2×Dic11C2×D811yescharacteristic
243C2×Dic11C2×D811yescharacteristic
244C2×Dic11C2×D811yescharacteristic
245D44—41no—
246D44—41no—
247D44—41no—
248D44—41no—
249C4×D11—82no—
250C4×D11—161no—
251Dic22—41no—
252Dic22—41no—
253Dic22—161no—
254C8×C11—21no—
255C8×C11H(5,𝔽2)11yescharacteristic
256C8×C11H(5,𝔽2)11yescharacteristic
257C11⋊C8—21no—
258C11⋊C8AGL(1,ℤ/8)12yes—
259C2×AGL(1,ℤ/8)—221no—
260C2×#135—111no—
261C22×D8C2×D1111yescharacteristic
262#542—221no—
263#535—221no—
264C2×Q32—111no—
265C2×SD32—111no—
266C2×SD32—111no—
267C2×SD32C2×D1111yescharacteristic
268C2×SD32C2×D1111yescharacteristic
269C2×D16—111no—
270C2×D16—111no—
271C2×D16—111no—
272#500—111no—
273#496—221no—
274#496—221no—
275#495—111no—
276#495—111no—
277#495—111no—
278#493—111no—
279#493—111no—
280#489—221no—
281#468—221no—
282#467C2×D1111yescharacteristic
283#466—111no—
284#440—221no—
285C4×Q16—111no—
286C4×D8—111no—
287#405—111no—
288C4⋊C16—111no—
289C4⋊C16—111no—
290#358—111no—
291#358—111no—
292#357—111no—
293#357—111no—
294#357—111no—
295#357—111no—
296#357C2×D1111yescharacteristic
297#357C2×D1111yescharacteristic
298C22⋊C16—111no—
299C22⋊C16C2×D1111yescharacteristic
300#346—111no—
301C4×C16—111no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—81no—
306C22×C11—81no—
307C22×C11—81no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11—164no—
312C22×C11C22×D811yescharacteristic
313C2×D11—81no—
314C2×D11—81no—
315C2×D11—81no—
316C2×D11—81no—
317C2×D11—81no—
318C2×D11—81no—
319C4×C11—21no—
320C4×C11—81no—
321C4×C11—81no—
322C4×C11#53511yescharacteristic
323C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
324Dic11—21no—
325Dic11—21no—
326Dic11—21no—
327Dic11—21no—
328Dic11—81no—
329Dic11—81no—
330C2×#41—221no—
331C22×D4—21no—
332AGL(1,ℤ/8)—444no—
333#135—441no—
334#135—441no—
335C2×Q16—111no—
336C2×Q16C22×D1111yescharacteristic
337C2×SD16—221no—
338C2×SD16—221no—
339C2×SD16—221no—
340C2×SD16—221no—
341C2×D8—21no—
342C2×D8—41no—
343C2×D8—41no—
344C2×D8—111no—
345C2×D8—111no—
346C2×D8—221no—
347C2×D8—221no—
348C2×D8C22×D1111yescharacteristic
349C2×D8C22×D1111yescharacteristic
350C2×M16—111no—
351C22×C8C22×D1111yescharacteristic
352C4⋊Q8—221no—
353#127—221no—
354#127—221no—
355#126—441no—
356#124—221no—
357#124—221no—
358#124—221no—
359#124—441no—
360#123—441no—
361C22⋊Q8—21no—
362C22⋊Q8—441no—
363#121—221no—
364#121—441no—
365#121—441no—
366#120—441no—
367#120—441no—
368C4×Q8—221no—
369C4×D4—221no—
370#117—111no—
371Q32—441no—
372SD32—41no—
373SD32—41no—
374SD32—441no—
375SD32—441no—
376D16—441no—
377D16—441no—
378D16—441no—
379C2×C16—111no—
380C2×C16—111no—
381C2×C16C22×D1111yescharacteristic
382C2×C16C22×D1111yescharacteristic
383#107—111no—
384#107—221no—
385#107C22×D1111yescharacteristic
386#103—21no—
387#103—221no—
388#102—221no—
389#102—221no—
390#97—111no—
391#97—111no—
392C4×C8—111no—
393C4×C8—111no—
394C2×C11—41no—
395C2×C11—161no—
396C2×C11—161no—
397C2×C11#320511yescharacteristic
398C2×C11#341511yescharacteristic
399C2×C11#341611yescharacteristic
400D11—161no—
401D11—161no—
402C24—41no—
403#41—442no—
404#41—442no—
405C2×Q8—21no—
406C2×Q8—221no—
407C2×Q8—441no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—42no—
411C2×D4—42no—
412C2×D4—41no—
413C2×D4—221no—
414C2×D4—221no—
415C2×D4—441no—
416C2×D4—441no—
417C2×D4—441no—
418C2×D4—441no—
419C2×D4—441no—
420C2×D4—441no—
421C22×C4—441no—
422C22×C4—441no—
423C22×C4D4×D1111yescharacteristic
424Q16—21no—
425Q16—21no—
426Q16—221no—
427Q16—221no—
428SD16—442no—
429SD16—442no—
430SD16—442no—
431SD16—442no—
432D8—21no—
433D8—21no—
434D8—21no—
435D8—21no—
436D8—42no—
437D8—221no—
438D8—221no—
439D8—221no—
440D8—221no—
441D8—442no—
442D8—442no—
443M16—222no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—111no—
447C2×C8—111no—
448C2×C8D4×D1111yescharacteristic
449C2×C8C23×D1111yescharacteristic
450C4⋊C4—21no—
451C4⋊C4—41no—
452C4⋊C4—111no—
453C4⋊C4—111no—
454C4⋊C4—221no—
455C4⋊C4—441no—
456C4⋊C4—441no—
457C22⋊C4—41no—
458C22⋊C4—111no—
459C22⋊C4—111no—
460C22⋊C4—441no—
461C22⋊C4—441no—
462C22⋊C4—441no—
463C22⋊C4—441no—
464C22⋊C4—441no—
465C22⋊C4—441no—
466C22⋊C4—441no—
467C22⋊C4—441no—
468C42—111no—
469C42—111no—
470C42—441no—
471C16—21no—
472C16—21no—
473C16—221no—
474C16—221no—
475C11#3379011yescharacteristic, complemented, Sylow
476C23—41no—
477C23—41no—
478C23—82no—
479C23—161no—
480C23—161no—
481C23—441no—
482C23—441no—
483C23D8×D1111yescharacteristic
484Q8—41no—
485Q8—41no—
486Q8—441no—
487Q8—441no—
488Q8—1761no—
489D4—41no—
490D4—41no—
491D4—41no—
492D4—41no—
493D4—82no—
494D4—441no—
495D4—441no—
496D4—441no—
497D4—441no—
498D4—882no—
499D4—1761no—
500D4—1761no—
501D4—1761no—
502D4—1761no—
503D4—1761no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—111no—
509C2×C4—111no—
510C2×C4—111no—
511C2×C4—111no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—882no—
515C2×C4—1761no—
516C2×C4D8×D1111yescharacteristic
517C2×C4C2×D4×D1111yescharacteristic
518C8—21no—
519C8—112no—
520C8—221no—
521C8#6703711yescharacteristic
522C8#6703711yescharacteristic
523C22—21no—
524C22—21no—
525C22—21no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—81no—
531C22—81no—
532C22—164no—
533C22—881no—
534C22—881no—
535C22—881no—
536C22—881no—
537C22—881no—
538C22—881no—
539C22C2×D8×D1111yescharacteristic
540C4—21no—
541C4—81no—
542C4—81no—
543C4—221no—
544C4—221no—
545C4—221no—
546C4—221no—
547C4—881no—
548C4—881no—
549C4#1062312311yescharacteristic
550C4D11×AGL(1,ℤ/8)11yescharacteristic
551C2—41no—
552C2—161no—
553C2—161no—
554C2—1761no—
555C2—1761no—
556C2#1307953211yescharacteristic
557C2#1308175611yescharacteristic
558C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2187C2
socleC22×C11C22×D8
hypercenter#2187D11
hypocenterC11#33790
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2187

Complements

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

NH ≅ G/Ntype
1. #13079256C2semidirect
2. #13079097C2semidirect
3. #13070881C2semidirect
4. #13070876C2semidirect
5. #13070851C2semidirect
6. #13070838C2semidirect
7. #13070676C2semidirect
8. #13070670C2semidirect
9. #13070654C2semidirect
10. #13070650C2semidirect
11. #13070554C2semidirect
12. #13070541C2semidirect
13. #13070528C2semidirect
14. #13070420C2semidirect
15. C11×#2187C2semidirect
24. #10622804C22semidirect
25. Q16×Dic11C22semidirect
26. C2×#66893C22semidirect
27. C2×#66892C22semidirect
39. C2×#66864C22semidirect
40. C2×D176C22semidirect
41. #10622487C22semidirect
42. #10622485C22semidirect
51. #10622147C22semidirect
52. #10622141C22semidirect
53. #10622140C22semidirect
54. Dic11⋊C16C22semidirect
55. Dic11⋊C16C22semidirect
56. C16×Dic11C22semidirect
57. #10622130C22semidirect
58. #10622129C22semidirect
208. #2187D11semidirect
475. C11#33790semidirect

Maximal subgroups

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

subgroupindex
#130792562
#130790972
#130708812
#130708762
#130708512
#130708382
#130706762
#130706702
#130706542
#130706502
#130705542
#130705412
#130705282
#130704202
C11×#21872
#3379011