Finite Group Databasebeta

← #14909839

Subgroups — #14909839

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#13079102C211yesmaximal, characteristic, complemented
2#13070883C211yesmaximal, characteristic, complemented
3#13070875C211yesmaximal, characteristic, complemented
4#13070855C211yesmaximal, characteristic, complemented
5#13070841C211yesmaximal, characteristic, complemented
6#13070678C211yesmaximal, characteristic, complemented
7#13070671C211yesmaximal, characteristic, complemented
8#13070656C211yesmaximal, characteristic, complemented
9#13070651C211yesmaximal, characteristic, complemented
10#13070554C211yesmaximal, characteristic, complemented
11#13070544C211yesmaximal, characteristic, complemented
12#13070537C211yesmaximal, characteristic, complemented
13#13070527C211yesmaximal, characteristic, complemented
14#13070423C211yesmaximal, characteristic, complemented
15C11×#3175C211yesmaximal, characteristic, complemented
16C11×#542—21no—
17C2×#66961—21no—
18C2×#66957C2211yescharacteristic
19C22×D88C2211yescharacteristic
20#10623056—21no—
21C11×#500C2211yescharacteristic, complemented
22C11×#495C2211yescharacteristic, complemented
23C11×#489—21no—
24C11×#468—21no—
25C11×#467C2211yescharacteristic
26C11×#466C2211yescharacteristic
27C11×#440—21no—
28C4×C11×Q16C2211yescharacteristic, complemented
29C4×C11×D8C2211yescharacteristic, complemented
30C11×#405C2211yescharacteristic
31C2×#66893C2211yescharacteristic, complemented
32C2×#66892C2211yescharacteristic
33C2×#66892C2211yescharacteristic
34C2×#66892C2211yescharacteristic, complemented
35C2×#66891C2211yescharacteristic, complemented
36C2×#66890C2211yescharacteristic
37C2×#66890C2211yescharacteristic
38C2×#66890C2211yescharacteristic, complemented
39#10622325—21no—
40#10622325—21no—
41#10622309C2211yescharacteristic
42#10622309C2211yescharacteristic
43#10622308C2211yescharacteristic
44#10622308C2211yescharacteristic
45C22⋊(C11⋊C16)C2211yescharacteristic
46C22⋊(C11⋊C16)C2211yescharacteristic
47#10622130C2211yescharacteristic, complemented
48#10622130C2211yescharacteristic, complemented
49#10622129C2211yescharacteristic
50#10622129C2211yescharacteristic
51#10622129C2211yescharacteristic
52#10622129C2211yescharacteristic
53#10622129C2211yescharacteristic, complemented
54#10622129C2211yescharacteristic, complemented
55C4⋊(C11⋊C16)C2211yescharacteristic, complemented
56C4⋊(C11⋊C16)C2211yescharacteristic, complemented
57#10622099C2211yescharacteristic, complemented
58C4×C11⋊C16C2211yescharacteristic, complemented
59C2×#4339—21no—
60C22×D44—21no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×SD16—21no—
63C2×C11×D8C2311yescharacteristic
64C2×C11×M16D411yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×C4⋊Q8—21no—
67C11×#126—41no—
68C11×#124—21no—
69C11×#124—41no—
70C11×#123—41no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8—41no—
73C11×#121—21no—
74C4×Q8×C11—21no—
75C4×D4×C11—21no—
76C11×#117D411yescharacteristic
77#66961—44no—
78C2×Dic44C2311yescharacteristic
79#66957—41no—
80#66957—41no—
81C2×D88—21no—
82C2×D88—21no—
83C2×D88—21no—
84C2×D88—41no—
85C2×D88—41no—
86C2×D88C2311yescharacteristic
87C2×D88C2311yescharacteristic
88C2×D88C2311yescharacteristic
89C2×#4314—21no—
90C2×#4314—21no—
91C2×#4314—21no—
92#66948—41no—
93#66948—41no—
94#66935—41no—
95#66935—41no—
96#66928—21no—
97#66928—21no—
98#66927—21no—
99#66927—21no—
100C11×#107—21no—
101C11×#107C2311yescharacteristic
102C11×#107C2311yescharacteristic
103C11×#103—21no—
104C11×#103—21no—
105C11×#102—21no—
106C11×#102—21no—
107C11×#97D411yescharacteristic
108C11×#97D411yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111#66893—41no—
112#66892—41no—
113#66892—41no—
114#66892—41no—
115#66891—41no—
116#66890—41no—
117#66890—41no—
118#66890—41no—
119C2×C11⋊C16C2311yescharacteristic
120C2×C11⋊C16C2311yescharacteristic
121C2×C11⋊C16C2311yescharacteristic
122C2×C11⋊C16C2311yescharacteristic
123#33790—111nomaximal, Sylow
124C23×D11—41no—
125C2×Q8×C11—21no—
126C2×Q8×C11—41no—
127C2×D4×C11—21no—
128C2×D4×C11—41no—
129C22×C4×C11—41no—
130C22×C4×C11C2×D411yescharacteristic
131C2×C22⋊D11—41no—
132#4339—42no—
133#4339—42no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—42no—
138C2×D44—42no—
139C2×D44—41no—
140C2×D44—41no—
141C2×D44—41no—
142C2×D44—41no—
143C2×D44—41no—
144C2×C4×D11—41no—
145C2×Dic22—21no—
146C11×Q16—21no—
147C11×Q16—21no—
148C11×SD16—42no—
149C11×D8—21no—
150C11×D8—21no—
151C11×M16—22no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11C2×D411yescharacteristic
155C2×C8×C11C2×D411yescharacteristic
156C2×C8×C11C2×D411yescharacteristic
157C2×C8×C11C2411yescharacteristic
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—41no—
161C11×C4⋊C4—41no—
162C11×C4⋊C4—41no—
163C11×C4⋊C4D811yescharacteristic
164C11×C4⋊C4D811yescharacteristic
165C11×C22⋊C4—41no—
166C11×C22⋊C4—41no—
167C11×C22⋊C4—41no—
168C11×C22⋊C4—41no—
169C11×C22⋊C4—41no—
170C11×C22⋊C4D811yescharacteristic
171C11×C22⋊C4D811yescharacteristic
172C42×C11—41no—
173C42×C11C2×D411yescharacteristic
174C42×C11C2×D411yescharacteristic
175(C2×D11)⋊C4—41no—
176(C2×D11)⋊C4—41no—
177(C2×D11)⋊C4—41no—
178(C2×D11)⋊C4—41no—
179Dic44—21no—
180Dic44—21no—
181D88—21no—
182D88—21no—
183D88—21no—
184D88—21no—
185D88—21no—
186D88—21no—
187D88—42no—
188D88—42no—
189D88—42no—
190#4314—42no—
191#4314—42no—
192#4314—42no—
193C11⋊C16—21no—
194C11⋊C16—21no—
195C11⋊C16—21no—
196C11⋊C16—21no—
197#3175D1111yescharacteristic, complemented
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#2187—111no—
209#2186—111no—
210#2184—111no—
211#2164—111no—
212C23×C11—41no—
213C23×C11C2×D811yescharacteristic
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—82no—
218C22×D11—161no—
219C22×D11—161no—
220Q8×C11—41no—
221Q8×C11—41no—
222Q8×C11—161no—
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—161no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—161no—
232C2×C4×C11C2×D811yescharacteristic
233C2×C4×C11C2×D811yescharacteristic
234C2×C4×C11C2×D811yescharacteristic
235C2×C4×C11C2×D811yescharacteristic
236C2×C4×C11C2×D811yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C22⋊D11—82no—
239C2×Dic11—41no—
240D44—41no—
241D44—41no—
242D44—41no—
243D44—41no—
244D44—41no—
245D44—41no—
246D44—82no—
247D44—161no—
248D44—161no—
249D44—161no—
250D44—161no—
251C4×D11—82no—
252Dic22—41no—
253Dic22—41no—
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)—221no—
260C2×#135—111no—
261C22×D8—111no—
262#542—21no—
263#535—221no—
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#500C2×D1111yescharacteristic, complemented
273#496—221no—
274#496—221no—
275#495—111no—
276#495—111no—
277#495C2×D1111yescharacteristic, complemented
278#493—111no—
279#493—111no—
280#489—21no—
281#468—21no—
282#467C2×D1111yescharacteristic
283#466C2×D1111yescharacteristic
284#440—21no—
285C4×Q16C2×D1111yescharacteristic, complemented
286C4×D8C2×D1111yescharacteristic, complemented
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×C11C22×D811yescharacteristic
309C2×D11—81no—
310C2×D11—81no—
311C2×D11—81no—
312C2×D11—81no—
313C2×D11—81no—
314C2×D11—81no—
315C2×D11—81no—
316C2×D11—81no—
317C2×D11—81no—
318C2×D11—164no—
319C4×C11—21no—
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—81no—
325C4×C11—81no—
326C4×C11—81no—
327C4×C11#53511yescharacteristic
328C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
329Dic11—81no—
330C2×#41—221no—
331C22×D4—221no—
332AGL(1,ℤ/8)—444no—
333#135—441no—
334#135—441no—
335C2×Q16—111no—
336C2×Q16C22×D1111yescharacteristic
337C2×SD16—21no—
338C2×SD16—221no—
339C2×SD16—221no—
340C2×SD16—221no—
341C2×D8—111no—
342C2×D8—111no—
343C2×D8—111no—
344C2×D8—221no—
345C2×D8—221no—
346C2×D8—221no—
347C2×D8—441no—
348C2×D8—441no—
349C2×D8C22×D1111yescharacteristic
350C2×M16C22⋊D1111yescharacteristic
351C22×C8C22×D1111yescharacteristic
352C4⋊Q8—21no—
353#127—221no—
354#127—221no—
355#126—41no—
356#124—21no—
357#124—41no—
358#124—221no—
359#124—221no—
360#123—41no—
361C22⋊Q8—21no—
362C22⋊Q8—41no—
363#121—21no—
364#121—441no—
365#121—441no—
366#120—441no—
367#120—441no—
368C4×Q8—21no—
369C4×D4—21no—
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—21no—
384#107C22×D1111yescharacteristic
385#107C22×D1111yescharacteristic
386#103—21no—
387#103—21no—
388#102—21no—
389#102—21no—
390#97C22⋊D1111yescharacteristic
391#97C22⋊D1111yescharacteristic
392C4×C8C22×D1111yescharacteristic
393C4×C8C22×D1111yescharacteristic
394C2×C11—41no—
395C2×C11—161no—
396C2×C11#320511yescharacteristic
397C2×C11#341511yescharacteristic
398C2×C11#341611yescharacteristic
399D11—161no—
400D11—161no—
401D11—161no—
402C24—441no—
403#41—442no—
404#41—442no—
405C2×Q8—21no—
406C2×Q8—41no—
407C2×Q8—221no—
408C2×D4—21no—
409C2×D4—41no—
410C2×D4—221no—
411C2×D4—221no—
412C2×D4—221no—
413C2×D4—442no—
414C2×D4—442no—
415C2×D4—441no—
416C2×D4—441no—
417C2×D4—441no—
418C2×D4—441no—
419C2×D4—441no—
420C2×D4—441no—
421C22×C4—41no—
422C22×C4—441no—
423C22×C4C2×C22⋊D1111yescharacteristic
424Q16—21no—
425Q16—21no—
426Q16—221no—
427Q16—221no—
428SD16—42no—
429SD16—442no—
430SD16—442no—
431SD16—442no—
432D8—21no—
433D8—21no—
434D8—221no—
435D8—221no—
436D8—221no—
437D8—221no—
438D8—221no—
439D8—221no—
440D8—442no—
441D8—442no—
442D8—442no—
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—21no—
451C4⋊C4—21no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4#432311yescharacteristic
456C4⋊C4#432311yescharacteristic
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—41no—
462C22⋊C4—441no—
463C22⋊C4—441no—
464C22⋊C4—441no—
465C22⋊C4—441no—
466C22⋊C4#432311yescharacteristic
467C22⋊C4#432311yescharacteristic
468C42—41no—
469C42C2×C22⋊D1111yescharacteristic
470C42C2×C22⋊D1111yescharacteristic
471C16—221no—
472C16—221no—
473C16—221no—
474C16—221no—
475C11#3379011yescharacteristic, complemented, Sylow
476C23—41no—
477C23—441no—
478C23—441no—
479C23—441no—
480C23—882no—
481C23—1761no—
482C23—1761no—
483C23C2×#432311yescharacteristic
484Q8—41no—
485Q8—41no—
486Q8—161no—
487Q8—441no—
488Q8—441no—
489D4—41no—
490D4—41no—
491D4—161no—
492D4—441no—
493D4—441no—
494D4—441no—
495D4—441no—
496D4—441no—
497D4—441no—
498D4—882no—
499D4—882no—
500D4—1761no—
501D4—1761no—
502D4—1761no—
503D4—1761no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—161no—
510C2×C4—441no—
511C2×C4—882no—
512C2×C4C2×#432311yescharacteristic
513C2×C4C2×#432311yescharacteristic
514C2×C4C2×#432311yescharacteristic
515C2×C4C2×#432311yescharacteristic
516C2×C4C2×#432311yescharacteristic
517C2×C4C22×C22⋊D1111yescharacteristic
518C8—21no—
519C8—21no—
520C8#6700212yes—
521C8#6704211yescharacteristic
522C8#6704211yescharacteristic
523C22—21no—
524C22—21no—
525C22—21no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—881no—
530C22—881no—
531C22—881no—
532C22—881no—
533C22—881no—
534C22—881no—
535C22—881no—
536C22—881no—
537C22—881no—
538C22—1764no—
539C22C22×#432311yescharacteristic
540C4—21no—
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—81no—
546C4—81no—
547C4—81no—
548C4—881no—
549C4C2×#6700211yescharacteristic
550C4#1062336111yescharacteristic
551C2—41no—
552C2—161no—
553C2—1761no—
554C2—1761no—
555C2—1761no—
556C2#1307953111yescharacteristic
557C2#1308175511yescharacteristic
558C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3175C2
socleC22×C11C22×D8
hypercenter#3175D11
hypocenterC11#33790
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3175

Complements

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

NH ≅ G/Ntype
1. #13079102C2semidirect
2. #13070883C2semidirect
3. #13070875C2semidirect
4. #13070855C2semidirect
5. #13070841C2semidirect
6. #13070678C2semidirect
7. #13070671C2semidirect
8. #13070656C2semidirect
9. #13070651C2semidirect
10. #13070554C2semidirect
11. #13070544C2semidirect
12. #13070537C2semidirect
13. #13070527C2semidirect
14. #13070423C2semidirect
15. C11×#3175C2semidirect
21. C11×#500C22semidirect
22. C11×#495C22semidirect
28. C4×C11×Q16C22semidirect
29. C4×C11×D8C22semidirect
31. C2×#66893C22semidirect
34. C2×#66892C22semidirect
35. C2×#66891C22semidirect
38. C2×#66890C22semidirect
47. #10622130C22semidirect
48. #10622130C22semidirect
53. #10622129C22semidirect
54. #10622129C22semidirect
55. C4⋊(C11⋊C16)C22semidirect
56. C4⋊(C11⋊C16)C22semidirect
57. #10622099C22semidirect
58. C4×C11⋊C16C22semidirect
197. #3175D11semidirect
272. #500C2×D11semidirect
277. #495C2×D11semidirect
285. C4×Q16C2×D11semidirect
286. C4×D8C2×D11semidirect
475. C11#33790semidirect

Maximal subgroups

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

subgroupindex
#130791022
#130708832
#130708752
#130708552
#130708412
#130706782
#130706712
#130706562
#130706512
#130705542
#130705442
#130705372
#130705272
#130704232
C11×#31752
#3379011