Finite Group Databasebeta

← #14909597

Subgroups — #14909597

Order 2816.

596 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078264C211yesmaximal, characteristic, complemented
2#13070821C211yesmaximal, characteristic, complemented
3#13070804C211yesmaximal, characteristic, complemented
4#13070801C211yesmaximal, characteristic, complemented
5#13070796C211yesmaximal, characteristic, complemented
6#13070731C211yesmaximal, characteristic, complemented
7#13070717C211yesmaximal, characteristic, complemented
8#13070714C211yesmaximal, characteristic, complemented
9#13070700C211yesmaximal, characteristic, complemented
10#13070544C211yesmaximal, characteristic, complemented
11#13070539C211yesmaximal, characteristic, complemented
12#13070539C211yesmaximal, characteristic, complemented
13#13070527C211yesmaximal, characteristic, complemented
14#13070230C211yesmaximal, characteristic, complemented
15C11×#3061C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic, complemented
17C2×C11×#131C2211yescharacteristic
18C11×#537—21no—
19#10623361—21no—
20C22×D88C2211yescharacteristic
21C11×#468—21no—
22C11×#468—21no—
23C11×#467C2211yescharacteristic
24C11×#467C2211yescharacteristic, complemented
25C11×#466C2211yescharacteristic
26C11×#466C2211yescharacteristic, complemented
27C2×C11×#107C2211yescharacteristic, complemented
28C11×#417—21no—
29C2×#66892C2211yescharacteristic
30C2×#66892C2211yescharacteristic
31C2×#66890C2211yescharacteristic
32C2×#66890C2211yescharacteristic
33#10622748—21no—
34#10622748—21no—
35#10622744—21no—
36#10622728C2211yescharacteristic
37#10622728C2211yescharacteristic
38#10622728C2211yescharacteristic
39#10622728C2211yescharacteristic
40#10622719C2211yescharacteristic
41C2×#66876C2211yescharacteristic, complemented
42C22×C11⋊C16C2211yescharacteristic, complemented
43#10622202C2211yescharacteristic, complemented
44#10622202C2211yescharacteristic, complemented
45#10622200C2211yescharacteristic, complemented
46#10622200C2211yescharacteristic, complemented
47C22⋊(C11⋊C16)C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49C22⋊(C11⋊C16)C2211yescharacteristic, complemented
50C22⋊(C11⋊C16)C2211yescharacteristic, complemented
51#10622129C2211yescharacteristic
52#10622129C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622129C2211yescharacteristic
55#10622128C2211yescharacteristic, complemented
56#10622128C2211yescharacteristic, complemented
57#10622127C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×C11×#41—21no—
60C2×C11×#41D411yescharacteristic
61C22×D44—21no—
62C11×#135—41no—
63C11×#135—41no—
64C2×C11×Q16C2311yescharacteristic
65C2×C11×SD16—21no—
66C2×C11×D8C2311yescharacteristic
67C11×#131—41no—
68C11×#131—41no—
69C2×C11×M16D411yescharacteristic
70C2×C11×M16D411yescharacteristic
71C2×C11×M16D411yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—41no—
78C11×#121—21no—
79C11×#121—21no—
80C11×#121—41no—
81C11×#121—41no—
82C11×#121—41no—
83C2×C11×C4⋊C4—21no—
84#67000—41no—
85#66993—41no—
86#66990—41no—
87#66990—41no—
88#66983—21no—
89#66983—21no—
90#66983—21no—
91#66983—21no—
92#66979—21no—
93C2×D88—21no—
94C2×D88—41no—
95C2×D88—41no—
96C2×D88C2311yescharacteristic
97C2×D88C2311yescharacteristic
98C11×#107—21no—
99C11×#107C2311yescharacteristic
100C11×#107C2311yescharacteristic
101C11×#103—21no—
102C11×#103—21no—
103C11×#102—21no—
104C11×#102—21no—
105#66892—41no—
106#66892—41no—
107#66890—41no—
108#66890—41no—
109#66885—21no—
110#66885—21no—
111#66885—21no—
112#66885—21no—
113#66882C2311yescharacteristic
114#66882C2311yescharacteristic
115#66881—21no—
116#66876—41no—
117C2×C11⋊C16—41no—
118C2×C11⋊C16C2311yescharacteristic
119C2×C11⋊C16C2311yescharacteristic
120C2×C11⋊C16C2311yescharacteristic
121C2×C11⋊C16C2311yescharacteristic
122#33764—111nomaximal, Sylow
123C23×D11—41no—
124C11×#41—41no—
125C11×#41—41no—
126C11×#41—42no—
127C11×#41—42no—
128C2×Q8×C11—21no—
129C2×Q8×C11D811yescharacteristic
130C2×D4×C11—21no—
131C2×D4×C11—41no—
132C2×D4×C11—41no—
133C2×D4×C11—41no—
134C2×D4×C11D811yescharacteristic
135C2×D4×C11D811yescharacteristic
136C2×D4×C11D811yescharacteristic
137C22×C4×C11—41no—
138C22×C4×C11—41no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C2×C22⋊D11—41no—
143C2×C22⋊D11—41no—
144C2×C22⋊D11—41no—
145C2×C22⋊D11—41no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—42no—
149C2×D44—42no—
150C2×D44—41no—
151C11×Q16—21no—
152C11×Q16—21no—
153C11×SD16—42no—
154C11×D8—21no—
155C11×D8—21no—
156C11×M16—41no—
157C11×M16—41no—
158C11×M16—41no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2411yescharacteristic
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—41no—
172C11×C4⋊C4—41no—
173C11×C4⋊C4—41no—
174C11×C22⋊C4—41no—
175C11×C22⋊C4—41no—
176C11×C22⋊C4—41no—
177C11×C22⋊C4—41no—
178C22⋊Dic11—41no—
179(C2×D11)⋊C4—41no—
180(C2×D11)⋊C4—41no—
181(C2×D11)⋊C4—41no—
182(C2×D11)⋊C4—41no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4×Dic11—41no—
186D88—21no—
187D88—21no—
188D88—21no—
189D88—21no—
190D88—42no—
191C11⋊C16—21no—
192C11⋊C16—21no—
193C11⋊C16—21no—
194C11⋊C16—21no—
195#3061D1111yescharacteristic, complemented
196#3058—111no—
197#2237—111no—
198#2234—111no—
199#2233—111no—
200#2232—111no—
201#2220—111no—
202#2218—111no—
203#2217—111no—
204#2215—111no—
205#2187—111no—
206#2186—111no—
207#2186—111no—
208#2184—111no—
209#2113—111no—
210C23×C11—41no—
211C23×C11C2×D811yescharacteristic
212C23×C11C2×D811yescharacteristic
213C23×C11C2×D811yescharacteristic
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—82no—
217C22×D11—161no—
218C22×D11—161no—
219Q8×C11—41no—
220Q8×C11—41no—
221Q8×C11—41no—
222D4×C11—41no—
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—41no—
226D4×C11—41no—
227D4×C11—82no—
228D4×C11—161no—
229D4×C11—161no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—82no—
240C2×C4×C11—161no—
241C2×C4×C11C2×D811yescharacteristic
242C2×C4×C11C2×D811yescharacteristic
243C2×C4×C11C2×D811yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C22⋊D11—161no—
246C22⋊D11—161no—
247C22⋊D11—161no—
248C22⋊D11—161no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251D44—41no—
252D44—41no—
253D44—41no—
254D44—41no—
255D44—82no—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11H(5,𝔽2)11yescharacteristic
260C8×C11H(5,𝔽2)11yescharacteristic
261C2×#135C2×D1111yescharacteristic, complemented
262C22×D8—111no—
263C2×#131C2×D1111yescharacteristic
264#537—21no—
265#535—221no—
266C2×SD32—111no—
267C2×SD32—111no—
268C2×D16—111no—
269C2×D16—111no—
270C2×M32—111no—
271C22×C16—111no—
272#469—221no—
273#469—221no—
274#468—21no—
275#468—21no—
276#467C2×D1111yescharacteristic
277#467C2×D1111yescharacteristic, complemented
278#466—111no—
279#466—111no—
280#466—111no—
281#466—111no—
282#466C2×D1111yescharacteristic
283#466C2×D1111yescharacteristic, complemented
284#427—111no—
285C2×#107C2×D1111yescharacteristic, complemented
286#418—221no—
287#417—21no—
288#367—111no—
289#367—111no—
290#366—111no—
291#366—111no—
292#358—111no—
293#358—111no—
294#357—111no—
295#357—111no—
296#357—111no—
297#357—111no—
298#357—111no—
299#357—111no—
300C22⋊C16—111no—
301C22⋊C16—111no—
302C22⋊C16—111no—
303C22⋊C16—111no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—21no—
311C22×C11—21no—
312C22×C11—21no—
313C22×C11—81no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11C22×D811yescharacteristic
317C2×D11—81no—
318C2×D11—81no—
319C2×D11—81no—
320C2×D11—81no—
321C2×D11—81no—
322C2×D11—81no—
323C2×D11—164no—
324C4×C11—21no—
325C4×C11—21no—
326C4×C11—21no—
327C4×C11—81no—
328C4×C11—81no—
329C4×C11—81no—
330C4×C11#53411yescharacteristic
331C4×C11#57511yescharacteristic
332Dic11—81no—
333Dic11—81no—
334C2×#41—21no—
335C2×#41C22⋊D1111yescharacteristic
336C22×D4—221no—
337#135—41no—
338#135—41no—
339C2×Q16C22×D1111yescharacteristic
340C2×SD16—21no—
341C2×D8—111no—
342C2×D8—111no—
343C2×D8—221no—
344C2×D8—441no—
345C2×D8—441no—
346C2×D8C22×D1111yescharacteristic
347#131—41no—
348#131—41no—
349C2×M16C22⋊D1111yescharacteristic
350C2×M16C22⋊D1111yescharacteristic
351C2×M16C22⋊D1111yescharacteristic
352C22×C8C22×D1111yescharacteristic
353C22×C8C22×D1111yescharacteristic
354C22×C8C22×D1111yescharacteristic
355#127—441no—
356#124—441no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—41no—
360#121—21no—
361#121—21no—
362#121—41no—
363#121—41no—
364#121—41no—
365#121—221no—
366#121—221no—
367#121—221no—
368#121—221no—
369#120—441no—
370#120—441no—
371#117—221no—
372C2×C4⋊C4—21no—
373SD32—441no—
374SD32—441no—
375D16—441no—
376D16—441no—
377M32—441no—
378C2×C16—111no—
379C2×C16—111no—
380C2×C16—111no—
381C2×C16—111no—
382C2×C16—441no—
383#107—21no—
384#107—111no—
385#107—111no—
386#107C22×D1111yescharacteristic
387#107C22×D1111yescharacteristic
388#106—221no—
389#103—21no—
390#103—21no—
391#102—21no—
392#102—21no—
393#102—221no—
394#102—221no—
395#102—221no—
396#102—221no—
397C2×C11—41no—
398C2×C11—41no—
399C2×C11—41no—
400C2×C11—161no—
401C2×C11#318611yescharacteristic
402C2×C11#341511yescharacteristic
403C2×C11#341611yescharacteristic
404D11—161no—
405D11—161no—
406C24—441no—
407#41—41no—
408#41—41no—
409#41—42no—
410#41—42no—
411C2×Q8—21no—
412C2×Q8#432311yescharacteristic
413C2×D4—21no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—442no—
420C2×D4—442no—
421C2×D4—441no—
422C2×D4—441no—
423C2×D4—441no—
424C2×D4—441no—
425C2×D4—441no—
426C2×D4#432311yescharacteristic
427C2×D4#432311yescharacteristic
428C2×D4#432311yescharacteristic
429C22×C4—41no—
430C22×C4—41no—
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434Q16—21no—
435Q16—21no—
436SD16—42no—
437D8—21no—
438D8—21no—
439D8—221no—
440D8—221no—
441D8—221no—
442D8—221no—
443D8—442no—
444M16—41no—
445M16—41no—
446M16—41no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8C2×C22⋊D1111yescharacteristic
454C2×C8C2×C22⋊D1111yescharacteristic
455C2×C8C2×C22⋊D1111yescharacteristic
456C2×C8C23×D1111yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—441no—
469C22⋊C4—441no—
470C22⋊C4—441no—
471C22⋊C4—441no—
472C22⋊C4—441no—
473C42—441no—
474C16—221no—
475C16—221no—
476C16—221no—
477C16—221no—
478C11#3376411yescharacteristic, complemented, Sylow
479C23—41no—
480C23—441no—
481C23—441no—
482C23—882no—
483C23—1761no—
484C23—1761no—
485C23C2×#432311yescharacteristic
486C23C2×#432311yescharacteristic
487C23C2×#432311yescharacteristic
488Q8—41no—
489Q8—41no—
490Q8—41no—
491D4—41no—
492D4—41no—
493D4—41no—
494D4—41no—
495D4—41no—
496D4—82no—
497D4—161no—
498D4—161no—
499D4—441no—
500D4—441no—
501D4—441no—
502D4—441no—
503D4—882no—
504D4—1761no—
505D4—1761no—
506D4—1761no—
507D4—1761no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—82no—
518C2×C4—161no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4C2×#432311yescharacteristic
522C2×C4C2×#432311yescharacteristic
523C2×C4C2×#432311yescharacteristic
524C2×C4C22×C22⋊D1111yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8#6703711yescharacteristic
529C8#6703711yescharacteristic
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—881no—
543C22—881no—
544C22—881no—
545C22—881no—
546C22—881no—
547C22—881no—
548C22—1764no—
549C22C22×#432311yescharacteristic
550C4—21no—
551C4—21no—
552C4—21no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4—881no—
557C4—881no—
558C4#1062333511yescharacteristic
559C4#1062335311yescharacteristic
560C2—41no—
561C2—41no—
562C2—41no—
563C2—161no—
564C2—1761no—
565C2—1761no—
566C2#1307936411yescharacteristic
567C2#1308175511yescharacteristic
568C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3061C2
socleC22×C11C22×D8
hypercenter#3061D11
hypocenterC11#33764
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #3061

Complements

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

NH ≅ G/Ntype
1. #13078264C2semidirect
2. #13070821C2semidirect
3. #13070804C2semidirect
4. #13070801C2semidirect
5. #13070796C2semidirect
6. #13070731C2semidirect
7. #13070717C2semidirect
8. #13070714C2semidirect
9. #13070700C2semidirect
10. #13070544C2semidirect
11. #13070539C2semidirect
12. #13070539C2semidirect
13. #13070527C2semidirect
14. #13070230C2semidirect
15. C11×#3061C2semidirect
16. C2×C11×#135C22semidirect
24. C11×#467C22semidirect
26. C11×#466C22semidirect
27. C2×C11×#107C22semidirect
41. C2×#66876C22semidirect
42. C22×C11⋊C16C22semidirect
43. #10622202C22semidirect
44. #10622202C22semidirect
45. #10622200C22semidirect
46. #10622200C22semidirect
49. C22⋊(C11⋊C16)C22semidirect
50. C22⋊(C11⋊C16)C22semidirect
55. #10622128C22semidirect
56. #10622128C22semidirect
57. #10622127C22semidirect
58. #10622127C22semidirect
195. #3061D11semidirect
261. C2×#135C2×D11semidirect
277. #467C2×D11semidirect
283. #466C2×D11semidirect
285. C2×#107C2×D11semidirect
478. C11#33764semidirect

Maximal subgroups

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

subgroupindex
#130782642
#130708212
#130708042
#130708012
#130707962
#130707312
#130707172
#130707142
#130707002
#130705442
#130705392
#130705272
#130702302
C11×#30612
#3376411