Finite Group Databasebeta

← #14909845

Subgroups — #14909845

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#13079255C211yesmaximal, characteristic, complemented
2#13070880C211yesmaximal, characteristic, complemented
3#13070875C211yesmaximal, characteristic, complemented
4#13070852C211yesmaximal, characteristic, complemented
5#13070839C211yesmaximal, characteristic, complemented
6#13070675C211yesmaximal, characteristic, complemented
7#13070668C211yesmaximal, characteristic, complemented
8#13070653C211yesmaximal, characteristic, complemented
9#13070648C211yesmaximal, characteristic, complemented
10#13070556C211yesmaximal, characteristic, complemented
11#13070545C211yesmaximal, characteristic, complemented
12#13070539C211yesmaximal, characteristic, complemented
13#13070528C211yesmaximal, characteristic, complemented
14#13070423C211yesmaximal, characteristic, complemented
15C11×#3155C211yesmaximal, characteristic, complemented
16C2×C11×AGL(1,ℤ/8)—21no—
17C2×C11×#135C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C11×#535—21no—
20#10623065—21no—
21C11×#496—21no—
22C11×#496—21no—
23C11×#495C2211yescharacteristic
24C11×#495C2211yescharacteristic
25C11×#493C2211yescharacteristic
26C11×#493C2211yescharacteristic
27C11×#405C2211yescharacteristic
28C2×#66893C2211yescharacteristic, complemented
29C2×#66892C2211yescharacteristic, complemented
30C2×#66891C2211yescharacteristic
31C2×#66891C2211yescharacteristic
32C2×#66891C2211yescharacteristic, complemented
33C2×#66890C2211yescharacteristic
34C2×#66890C2211yescharacteristic
35C2×#66890C2211yescharacteristic, complemented
36#10622747—21no—
37#10622729C2211yescharacteristic
38#10622728C2211yescharacteristic
39#10622327—21no—
40#10622323—21no—
41C4×Dic44C2211yescharacteristic, complemented
42#10622309C2211yescharacteristic, complemented
43C4×D88C2211yescharacteristic, complemented
44#10622295C2211yescharacteristic, complemented
45#10622202C2211yescharacteristic, complemented
46#10622202C2211yescharacteristic, complemented
47#10622200C2211yescharacteristic
48#10622200C2211yescharacteristic
49#10622200C2211yescharacteristic
50#10622200C2211yescharacteristic
51#10622200C2211yescharacteristic, complemented
52#10622200C2211yescharacteristic, complemented
53C22⋊(C11⋊C16)C2211yescharacteristic
54C22⋊(C11⋊C16)C2211yescharacteristic
55C4⋊(C11⋊C16)C2211yescharacteristic, complemented
56C4⋊(C11⋊C16)C2211yescharacteristic, complemented
57#10622099C2211yescharacteristic, complemented
58C4×C11⋊C16C2211yescharacteristic, complemented
59C2×C11×#41—21no—
60C22×D4×C11—21no—
61C11×AGL(1,ℤ/8)—44no—
62C11×#135—41no—
63C11×#135—41no—
64C2×C11×Q16C2311yescharacteristic
65C2×C11×SD16—21no—
66C2×C11×SD16—21no—
67C2×C11×SD16—21no—
68C2×C11×D8—21no—
69C2×C11×D8—21no—
70C2×C11×D8—21no—
71C2×C11×D8—41no—
72C2×C11×D8—41no—
73C2×C11×D8C2311yescharacteristic
74C2×C11×D8C2311yescharacteristic
75C2×C11×D8C2311yescharacteristic
76C2×C11×M16D411yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C11×#127—21no—
79C11×#127—21no—
80C11×#124—21no—
81C11×#124—21no—
82C11×#121—41no—
83C11×#121—41no—
84C11×#120—41no—
85C11×#120—41no—
86C11×#117D411yescharacteristic
87#66983—21no—
88#66977—21no—
89C2×Dic44C2311yescharacteristic
90C2×D88C2311yescharacteristic
91C2×#4314—21no—
92#66951—41no—
93#66949—41no—
94#66938—41no—
95#66936—41no—
96#66928—21no—
97C4×D44—21no—
98#66922—21no—
99C4×Dic22—21no—
100C11×#97D411yescharacteristic
101C11×#97D411yescharacteristic
102C4×C8×C11C2311yescharacteristic
103C4×C8×C11C2311yescharacteristic
104#66893—41no—
105#66892—41no—
106#66891—41no—
107#66891—41no—
108#66891—41no—
109#66890—41no—
110#66890—41no—
111#66890—41no—
112#66885—21no—
113#66885—21no—
114#66882—21no—
115#66882C2311yescharacteristic
116#66882C2311yescharacteristic
117#66880—21no—
118#66880—21no—
119C2×C11⋊C16C2311yescharacteristic
120C2×C11⋊C16C2311yescharacteristic
121C2×C11⋊C16C2311yescharacteristic
122C2×C11⋊C16C2311yescharacteristic
123#33790—111nomaximal, Sylow
124C24×C11—41no—
125C11×#41—42no—
126C11×#41—42no—
127C2×Q8×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—42no—
132C2×D4×C11—42no—
133C2×D4×C11—41no—
134C2×D4×C11—41no—
135C2×D4×C11—41no—
136C2×D4×C11—41no—
137C2×D4×C11—41no—
138C2×D4×C11—41no—
139C22×C4×C11—41no—
140C22×C4×C11C2×D411yescharacteristic
141C2×C22⋊D11—41no—
142C2×D44—21no—
143C2×C4×D11—41no—
144C2×Dic22—21no—
145C2×Dic22—41no—
146C11×Q16—21no—
147C11×Q16—21no—
148C11×SD16—42no—
149C11×SD16—42no—
150C11×SD16—42no—
151C11×D8—21no—
152C11×D8—21no—
153C11×D8—21no—
154C11×D8—21no—
155C11×D8—21no—
156C11×D8—21no—
157C11×D8—42no—
158C11×D8—42no—
159C11×D8—42no—
160C11×M16—22no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11C2×D411yescharacteristic
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2411yescharacteristic
167C11×C4⋊C4D811yescharacteristic
168C11×C4⋊C4D811yescharacteristic
169C11×C22⋊C4—41no—
170C11×C22⋊C4—41no—
171C11×C22⋊C4—41no—
172C11×C22⋊C4—41no—
173C11×C22⋊C4D811yescharacteristic
174C11×C22⋊C4D811yescharacteristic
175C42×C11C2×D411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C22⋊Dic11—41no—
178(C2×D11)⋊C4—41no—
179(C2×D11)⋊C4—41no—
180(C2×D11)⋊C4—41no—
181(C2×D11)⋊C4—41no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—41no—
185Dic11⋊C4—41no—
186Dic11⋊C4—41no—
187C4×Dic11—41no—
188Dic44—21no—
189Dic44—21no—
190D88—21no—
191D88—21no—
192#4314—42no—
193C11⋊C16—21no—
194C11⋊C16—21no—
195C11⋊C16—21no—
196C11⋊C16—21no—
197#3175—111no—
198#3155D1111yescharacteristic, complemented
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#2187—111no—
209#2186—111no—
210#2184—111no—
211#2164—111no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—82no—
216C23×C11—161no—
217C23×C11—161no—
218C23×C11C2×D811yescharacteristic
219C22×D11—41no—
220Q8×C11—41no—
221Q8×C11—41no—
222D4×C11—41no—
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—41no—
226D4×C11—41no—
227D4×C11—41no—
228D4×C11—82no—
229D4×C11—82no—
230D4×C11—161no—
231D4×C11—161no—
232D4×C11—161no—
233D4×C11—161no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—41no—
237C2×C4×C11—82no—
238C2×C4×C11C2×D811yescharacteristic
239C2×C4×C11C2×D811yescharacteristic
240C2×C4×C11C2×D811yescharacteristic
241C2×C4×C11C2×D811yescharacteristic
242C2×C4×C11C2×D811yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C22⋊D11—161no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248D44—41no—
249D44—41no—
250C4×D11—161no—
251Dic22—41no—
252Dic22—41no—
253Dic22—161no—
254C8×C11—21no—
255C8×C11—21no—
256C8×C11AGL(1,ℤ/8)12yes—
257C8×C11H(5,𝔽2)11yescharacteristic
258C8×C11H(5,𝔽2)11yescharacteristic
259C2×AGL(1,ℤ/8)—21no—
260C2×#135C2×D1111yescharacteristic
261C22×D8C2×D1111yescharacteristic
262#542—221no—
263#535—21no—
264C2×Q32—111no—
265C2×SD32—111no—
266C2×SD32—111no—
267C2×SD32—111no—
268C2×SD32—111no—
269C2×D16—111no—
270C2×D16—111no—
271C2×D16—111no—
272#500—111no—
273#496—21no—
274#496—21no—
275#495—111no—
276#495C2×D1111yescharacteristic
277#495C2×D1111yescharacteristic
278#493C2×D1111yescharacteristic
279#493C2×D1111yescharacteristic
280#489—221no—
281#468—221no—
282#467—111no—
283#466—111no—
284#440—221no—
285C4×Q16—111no—
286C4×D8—111no—
287#405C2×D1111yescharacteristic
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#357—111no—
297#357—111no—
298C22⋊C16—111no—
299C22⋊C16—111no—
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—81no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11—164no—
315C22×C11C22×D811yescharacteristic
316C2×D11—81no—
317C2×D11—81no—
318C2×D11—81no—
319C4×C11—21no—
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—81no—
325C4×C11#53511yescharacteristic
326C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
327Dic11—81no—
328Dic11—81no—
329Dic11—81no—
330C2×#41—21no—
331C22×D4—21no—
332AGL(1,ℤ/8)—44no—
333#135—41no—
334#135—41no—
335C2×Q16—111no—
336C2×Q16C22×D1111yescharacteristic
337C2×SD16—21no—
338C2×SD16—21no—
339C2×SD16—21no—
340C2×SD16—221no—
341C2×D8—21no—
342C2×D8—21no—
343C2×D8—21no—
344C2×D8—41no—
345C2×D8—41no—
346C2×D8—111no—
347C2×D8C22×D1111yescharacteristic
348C2×D8C22×D1111yescharacteristic
349C2×D8C22×D1111yescharacteristic
350C2×M16C22⋊D1111yescharacteristic
351C22×C8C22×D1111yescharacteristic
352C4⋊Q8—221no—
353#127—21no—
354#127—21no—
355#126—441no—
356#124—21no—
357#124—21no—
358#124—221no—
359#124—441no—
360#123—441no—
361C22⋊Q8—221no—
362C22⋊Q8—441no—
363#121—41no—
364#121—41no—
365#121—221no—
366#120—41no—
367#120—41no—
368C4×Q8—221no—
369C4×D4—221no—
370#117C22⋊D1111yescharacteristic
371Q32—441no—
372SD32—441no—
373SD32—441no—
374SD32—441no—
375SD32—441no—
376D16—441no—
377D16—441no—
378D16—441no—
379C2×C16—111no—
380C2×C16—111no—
381C2×C16—111no—
382C2×C16—111no—
383#107—111no—
384#107—111no—
385#107—221no—
386#103—221no—
387#103—221no—
388#102—221no—
389#102—221no—
390#97C22⋊D1111yescharacteristic
391#97C22⋊D1111yescharacteristic
392C4×C8C22×D1111yescharacteristic
393C4×C8C22×D1111yescharacteristic
394C2×C11—41no—
395C2×C11—161no—
396C2×C11—161no—
397C2×C11—161no—
398C2×C11#320511yescharacteristic
399C2×C11#341511yescharacteristic
400C2×C11#341611yescharacteristic
401D11—161no—
402C24—41no—
403#41—42no—
404#41—42no—
405C2×Q8—21no—
406C2×Q8—221no—
407C2×Q8—441no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—42no—
412C2×D4—42no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—221no—
420C2×D4—441no—
421C22×C4—41no—
422C22×C4—441no—
423C22×C4C2×C22⋊D1111yescharacteristic
424Q16—21no—
425Q16—21no—
426Q16—221no—
427Q16—221no—
428SD16—42no—
429SD16—42no—
430SD16—42no—
431SD16—442no—
432D8—21no—
433D8—21no—
434D8—21no—
435D8—21no—
436D8—21no—
437D8—21no—
438D8—42no—
439D8—42no—
440D8—42no—
441D8—221no—
442D8—221no—
443M16—22no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8C2×C22⋊D1111yescharacteristic
447C2×C8C2×C22⋊D1111yescharacteristic
448C2×C8C2×C22⋊D1111yescharacteristic
449C2×C8C23×D1111yescharacteristic
450C4⋊C4—221no—
451C4⋊C4—221no—
452C4⋊C4—441no—
453C4⋊C4—441no—
454C4⋊C4—441no—
455C4⋊C4#432311yescharacteristic
456C4⋊C4#432311yescharacteristic
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—441no—
462C22⋊C4—441no—
463C22⋊C4—441no—
464C22⋊C4—441no—
465C22⋊C4—441no—
466C22⋊C4#432311yescharacteristic
467C22⋊C4#432311yescharacteristic
468C42—441no—
469C42C2×C22⋊D1111yescharacteristic
470C42C2×C22⋊D1111yescharacteristic
471C16—221no—
472C16—221no—
473C16—221no—
474C16—221no—
475C11#3379011yescharacteristic, complemented, Sylow
476C23—41no—
477C23—41no—
478C23—41no—
479C23—82no—
480C23—161no—
481C23—161no—
482C23—441no—
483C23C2×#432311yescharacteristic
484Q8—41no—
485Q8—41no—
486Q8—441no—
487Q8—441no—
488Q8—1761no—
489D4—41no—
490D4—41no—
491D4—41no—
492D4—41no—
493D4—41no—
494D4—41no—
495D4—82no—
496D4—82no—
497D4—161no—
498D4—161no—
499D4—161no—
500D4—161no—
501D4—441no—
502D4—441no—
503D4—1761no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—82no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—1761no—
512C2×C4C2×#432311yescharacteristic
513C2×C4C2×#432311yescharacteristic
514C2×C4C2×#432311yescharacteristic
515C2×C4C2×#432311yescharacteristic
516C2×C4C2×#432311yescharacteristic
517C2×C4C22×C22⋊D1111yescharacteristic
518C8—21no—
519C8—21no—
520C8#6698512yes—
521C8#6703711yescharacteristic
522C8#6703711yescharacteristic
523C22—21no—
524C22—21no—
525C22—21no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—81no—
531C22—81no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—164no—
536C22—881no—
537C22—881no—
538C22—881no—
539C22C22×#432311yescharacteristic
540C4—21no—
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—81no—
546C4—881no—
547C4—881no—
548C4—881no—
549C4C2×#6698511yescharacteristic
550C4#1062333611yescharacteristic
551C2—41no—
552C2—161no—
553C2—161no—
554C2—161no—
555C2—1761no—
556C2#1307953411yescharacteristic
557C2#1308175511yescharacteristic
558C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3155C2
socleC22×C11C22×D8
hypercenter#3155D11
hypocenterC11#33790
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3155

Complements

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

NH ≅ G/Ntype
1. #13079255C2semidirect
2. #13070880C2semidirect
3. #13070875C2semidirect
4. #13070852C2semidirect
5. #13070839C2semidirect
6. #13070675C2semidirect
7. #13070668C2semidirect
8. #13070653C2semidirect
9. #13070648C2semidirect
10. #13070556C2semidirect
11. #13070545C2semidirect
12. #13070539C2semidirect
13. #13070528C2semidirect
14. #13070423C2semidirect
15. C11×#3155C2semidirect
28. C2×#66893C22semidirect
29. C2×#66892C22semidirect
32. C2×#66891C22semidirect
35. C2×#66890C22semidirect
41. C4×Dic44C22semidirect
42. #10622309C22semidirect
43. C4×D88C22semidirect
44. #10622295C22semidirect
45. #10622202C22semidirect
46. #10622202C22semidirect
51. #10622200C22semidirect
52. #10622200C22semidirect
55. C4⋊(C11⋊C16)C22semidirect
56. C4⋊(C11⋊C16)C22semidirect
57. #10622099C22semidirect
58. C4×C11⋊C16C22semidirect
198. #3155D11semidirect
475. C11#33790semidirect

Maximal subgroups

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

subgroupindex
#130792552
#130708802
#130708752
#130708522
#130708392
#130706752
#130706682
#130706532
#130706482
#130705562
#130705452
#130705392
#130705282
#130704232
C11×#31552
#3379011