Finite Group Databasebeta

← #14909599

Subgroups — #14909599

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#13078281C211yesmaximal, characteristic, complemented
2#13078260C211yesmaximal, characteristic, complemented
3#13070825C211yesmaximal, characteristic, complemented
4#13070804C211yesmaximal, characteristic, complemented
5#13070800C211yesmaximal, characteristic, complemented
6#13070795C211yesmaximal, characteristic, complemented
7#13070728C211yesmaximal, characteristic, complemented
8#13070716C211yesmaximal, characteristic, complemented
9#13070711C211yesmaximal, characteristic, complemented
10#13070699C211yesmaximal, characteristic, complemented
11#13070545C211yesmaximal, characteristic, complemented
12#13070536C211yesmaximal, characteristic, complemented
13#13070536C211yesmaximal, characteristic, complemented
14#13070228C211yesmaximal, characteristic, complemented
15C11×#2184C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17#10623336—21no—
18C2×#66965C2211yescharacteristic, complemented
19C2×#66954C2211yescharacteristic
20#10623139—21no—
21C2×C11×D16C2211yescharacteristic
22C2×C11×D16C2211yescharacteristic
23C11×#466C2211yescharacteristic
24#10622828—21no—
25#10622772—21no—
26#10622772—21no—
27#10622770C2211yescharacteristic
28#10622770C2211yescharacteristic
29#10622770C2211yescharacteristic
30#10622770C2211yescharacteristic
31#10622770C2211yescharacteristic, complemented
32C2×#66891C2211yescharacteristic
33C2×#66891C2211yescharacteristic
34#10622729C2211yescharacteristic
35#10622719C2211yescharacteristic
36#10622655—21no—
37C2×#66862C2211yescharacteristic, complemented
38C2×C16×D11C2211yescharacteristic, complemented
39#10622500C2211yescharacteristic, complemented
40D11×#107C2211yescharacteristic, complemented
41#10622393—21no—
42#10622384—21no—
43C11×#357C2211yescharacteristic
44C11×#357C2211yescharacteristic
45C11×C22⋊C16C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622200C2211yescharacteristic, complemented
49#10622200C2211yescharacteristic, complemented
50C22⋊(C11⋊C16)C2211yescharacteristic
51(C2×D11)⋊C16C2211yescharacteristic, complemented
52(C2×D11)⋊C16C2211yescharacteristic, complemented
53#10622143C2211yescharacteristic, complemented
54#10622142C2211yescharacteristic, complemented
55#10622141C2211yescharacteristic, complemented
56#10622141C2211yescharacteristic, complemented
57#10622128C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C22×D4×C11—21no—
60C2×#4341—21no—
61C2×#4339D411yescharacteristic
62C2×C11×D8—21no—
63C2×C11×D8—41no—
64C2×C11×D8—41no—
65C2×C11×D8C2311yescharacteristic
66C2×C11×D8C2311yescharacteristic
67C2×C11×D8C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×#121—21no—
70#67006—41no—
71#67006—41no—
72#66993—41no—
73#66992—41no—
74#66991—21no—
75#66991—21no—
76#66991—21no—
77#66991—21no—
78#66991—21no—
79#66991—41no—
80#66989—41no—
81C2×#4324—21no—
82#66979—21no—
83#66977—21no—
84C2×#4318D411yescharacteristic
85#66965—41no—
86#66965—41no—
87C2×Dic44C2311yescharacteristic
88#66954—41no—
89#66954—41no—
90C2×#4313D411yescharacteristic
91C2×#4313D411yescharacteristic
92C2×C8×D11C2311yescharacteristic
93C2×C8×D11C2311yescharacteristic
94#66950—21no—
95C4⋊C4×D11—21no—
96#66937—41no—
97#66931—41no—
98C11×D16—41no—
99C11×D16—41no—
100C2×C11×C16C2311yescharacteristic
101C2×C11×C16C2311yescharacteristic
102C11×#107C2311yescharacteristic
103C11×#102—21no—
104#66896—21no—
105#66896—21no—
106#66896—21no—
107#66896—21no—
108#66896—21no—
109#66891—41no—
110#66891—41no—
111#66882C2311yescharacteristic
112#66882C2311yescharacteristic
113#66882C2311yescharacteristic
114#66881—21no—
115#66880—21no—
116C2×C11⋊C16C2311yescharacteristic
117C2×C11⋊C16C2311yescharacteristic
118#66874—21no—
119#66871—21no—
120#66862—41no—
121C16×D11—41no—
122#33764—111nomaximal, Sylow
123C24×C11—41no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11—41no—
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—
138C2×C22⋊D11D811yescharacteristic
139C2×C22⋊D11D811yescharacteristic
140C22×Dic11—41no—
141#4341—42no—
142#4341—42no—
143#4339—41no—
144#4339—41no—
145C2×D44D811yescharacteristic
146C2×C4×D11—41no—
147C2×C4×D11C2×D411yescharacteristic
148C2×C4×D11C2×D411yescharacteristic
149C2×Dic22—21no—
150C2×Dic22D811yescharacteristic
151C11×D8—21no—
152C11×D8—21no—
153C11×D8—21no—
154C11×D8—21no—
155C11×D8—21no—
156C11×D8—21no—
157C11×D8—42no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11C2×D411yescharacteristic
161C2×C8×C11C2411yescharacteristic
162C11×C4⋊C4—21no—
163C11×C22⋊C4—41no—
164C22⋊Dic11—41no—
165C22⋊Dic11—41no—
166C22⋊Dic11—41no—
167C22⋊Dic11—41no—
168C22⋊Dic11—41no—
169C22⋊Dic11—41no—
170C22⋊Dic11—41no—
171#4324—42no—
172(C2×D11)⋊C4—41no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—41no—
177Dic11⋊C4—41no—
178Dic11⋊C4—41no—
179C4×Dic11—41no—
180#4318—41no—
181C2×C11⋊C8C2×D411yescharacteristic
182C2×C11⋊C8C2×D411yescharacteristic
183Dic44—21no—
184Dic44—21no—
185#4313—41no—
186#4313—41no—
187C8×D11—21no—
188C8×D11—21no—
189C8×D11—21no—
190C8×D11—21no—
191C11×C16—21no—
192C11×C16—21no—
193C11⋊C16—21no—
194C11⋊C16—21no—
195#3061—111no—
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#2184D1111yescharacteristic, complemented
209#2113—111no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—82no—
214C23×C11—161no—
215C23×C11—161no—
216C23×C11C2×D811yescharacteristic
217C22×D11C2×D811yescharacteristic
218C22×D11C2×D811yescharacteristic
219D4×C11—41no—
220D4×C11—41no—
221D4×C11—41no—
222D4×C11—41no—
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—82no—
226D4×C11—161no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—41no—
230C2×C4×C11C2×D811yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C22⋊D11—41no—
233C22⋊D11—41no—
234C22⋊D11—82no—
235C22⋊D11—161no—
236C22⋊D11—161no—
237C22⋊D11—161no—
238C22⋊D11—161no—
239C22⋊D11—161no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—82no—
245C2×Dic11C2×D811yescharacteristic
246C2×Dic11C2×D811yescharacteristic
247D44—41no—
248C4×D11—21no—
249C4×D11—21no—
250C4×D11—21no—
251C4×D11—21no—
252C4×D11—161no—
253Dic22—41no—
254Dic22—41no—
255Dic22—41no—
256C8×C11—21no—
257C8×C11H(5,𝔽2)11yescharacteristic
258C8×C11H(5,𝔽2)11yescharacteristic
259C11⋊C8—21no—
260C11⋊C8—21no—
261C2×#135—111no—
262C22×D8C2×D1111yescharacteristic
263C2×#131—111no—
264#537—221no—
265#535—221no—
266C2×SD32—111no—
267C2×SD32—111no—
268C2×D16C2×D1111yescharacteristic
269C2×D16C2×D1111yescharacteristic
270C2×M32—111no—
271C22×C16—111no—
272#469—221no—
273#469—221no—
274#468—221no—
275#468—221no—
276#467—111no—
277#467—111no—
278#466—111no—
279#466—111no—
280#466—111no—
281#466—111no—
282#466—111no—
283#466C2×D1111yescharacteristic
284#427—111no—
285C2×#107—111no—
286#418—221no—
287#417—221no—
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#357C2×D1111yescharacteristic
299#357C2×D1111yescharacteristic
300C22⋊C16—111no—
301C22⋊C16—111no—
302C22⋊C16—111no—
303C22⋊C16C2×D1111yescharacteristic
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—81no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11—164no—
317C22×C11C22×D811yescharacteristic
318C2×D11—21no—
319C2×D11—21no—
320C2×D11—21no—
321C2×D11—21no—
322C2×D11—21no—
323C2×D11—21no—
324C4×C11—21no—
325C4×C11—81no—
326C4×C11#53411yescharacteristic
327C4×C11#57511yescharacteristic
328Dic11—21no—
329Dic11—21no—
330Dic11—81no—
331Dic11—81no—
332Dic11—81no—
333Dic11—81no—
334C2×#41—111no—
335C2×#41—221no—
336C22×D4—21no—
337#135—441no—
338#135—441no—
339C2×Q16—111no—
340C2×SD16—221no—
341C2×D8—21no—
342C2×D8—41no—
343C2×D8—41no—
344C2×D8C22×D1111yescharacteristic
345C2×D8C22×D1111yescharacteristic
346C2×D8C22×D1111yescharacteristic
347#131—441no—
348#131—441no—
349C2×M16—111no—
350C2×M16—111no—
351C2×M16—111no—
352C22×C8—111no—
353C22×C8—111no—
354C22×C8C22×D1111yescharacteristic
355#127—441no—
356#124—441no—
357C22⋊Q8—221no—
358C22⋊Q8—221no—
359C22⋊Q8—441no—
360#121—21no—
361#121—221no—
362#121—221no—
363#121—221no—
364#121—221no—
365#121—221no—
366#121—441no—
367#121—441no—
368#121—441no—
369#120—441no—
370#120—441no—
371#117—221no—
372C2×C4⋊C4—221no—
373SD32—441no—
374SD32—441no—
375D16—41no—
376D16—41no—
377M32—441no—
378C2×C16—111no—
379C2×C16—111no—
380C2×C16—441no—
381C2×C16C22×D1111yescharacteristic
382C2×C16C22×D1111yescharacteristic
383#107—111no—
384#107—111no—
385#107—111no—
386#107—221no—
387#107C22×D1111yescharacteristic
388#106—221no—
389#103—221no—
390#103—221no—
391#102—21no—
392#102—221no—
393#102—221no—
394#102—221no—
395#102—221no—
396#102—221no—
397C2×C11—41no—
398C2×C11—161no—
399C2×C11—161no—
400C2×C11—161no—
401C2×C11#318611yescharacteristic
402C2×C11#341511yescharacteristic
403C2×C11#341611yescharacteristic
404D11—41no—
405D11—41no—
406C24—41no—
407#41—441no—
408#41—441no—
409#41—442no—
410#41—442no—
411C2×Q8—111no—
412C2×Q8—221no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—111no—
421C2×D4—111no—
422C2×D4—111no—
423C2×D4—441no—
424C2×D4—441no—
425C2×D4—441no—
426C2×D4—441no—
427C2×D4—441no—
428C2×D4—441no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—441no—
432C22×C4—441no—
433C22×C4D4×D1111yescharacteristic
434Q16—221no—
435Q16—221no—
436SD16—442no—
437D8—21no—
438D8—21no—
439D8—21no—
440D8—21no—
441D8—21no—
442D8—21no—
443D8—42no—
444M16—441no—
445M16—441no—
446M16—441no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—111no—
450C2×C8—111no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8D4×D1111yescharacteristic
456C2×C8C23×D1111yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—441no—
462C4⋊C4—441no—
463C4⋊C4—441no—
464C22⋊C4—41no—
465C22⋊C4—441no—
466C22⋊C4—441no—
467C22⋊C4—441no—
468C22⋊C4—441no—
469C22⋊C4—441no—
470C22⋊C4—441no—
471C22⋊C4—441no—
472C22⋊C4—441no—
473C42—441no—
474C16—21no—
475C16—21no—
476C16—221no—
477C16—221no—
478C11#3376411yescharacteristic, complemented, Sylow
479C23—41no—
480C23—41no—
481C23—41no—
482C23—82no—
483C23—111no—
484C23—111no—
485C23—161no—
486C23—161no—
487C23D8×D1111yescharacteristic
488Q8—441no—
489Q8—441no—
490Q8—441no—
491D4—41no—
492D4—41no—
493D4—41no—
494D4—41no—
495D4—41no—
496D4—41no—
497D4—82no—
498D4—161no—
499D4—441no—
500D4—441no—
501D4—441no—
502D4—882no—
503D4—1761no—
504D4—1761no—
505D4—1761no—
506D4—1761no—
507D4—1761no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—111no—
512C2×C4—111no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—882no—
522C2×C4—1761no—
523C2×C4D8×D1111yescharacteristic
524C2×C4C2×D4×D1111yescharacteristic
525C8—21no—
526C8—221no—
527C8—221no—
528C8#6703711yescharacteristic
529C8#6703711yescharacteristic
530C22—21no—
531C22—21no—
532C22—21no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—164no—
543C22—221no—
544C22—221no—
545C22—221no—
546C22—221no—
547C22—221no—
548C22—221no—
549C22C2×D8×D1111yescharacteristic
550C4—21no—
551C4—81no—
552C4—221no—
553C4—221no—
554C4—881no—
555C4—881no—
556C4—881no—
557C4—881no—
558C4#1062312011yescharacteristic
559C4#1062330411yescharacteristic
560C2—41no—
561C2—161no—
562C2—161no—
563C2—161no—
564C2—441no—
565C2—441no—
566C2#1307936511yescharacteristic
567C2#1308175311yescharacteristic
568C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2184C2
socleC22×C11C22×D8
hypercenter#2184D11
hypocenterC11#33764
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2184

Complements

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

NH ≅ G/Ntype
1. #13078281C2semidirect
2. #13078260C2semidirect
3. #13070825C2semidirect
4. #13070804C2semidirect
5. #13070800C2semidirect
6. #13070795C2semidirect
7. #13070728C2semidirect
8. #13070716C2semidirect
9. #13070711C2semidirect
10. #13070699C2semidirect
11. #13070545C2semidirect
12. #13070536C2semidirect
13. #13070536C2semidirect
14. #13070228C2semidirect
15. C11×#2184C2semidirect
18. C2×#66965C22semidirect
31. #10622770C22semidirect
37. C2×#66862C22semidirect
38. C2×C16×D11C22semidirect
39. #10622500C22semidirect
40. D11×#107C22semidirect
48. #10622200C22semidirect
49. #10622200C22semidirect
51. (C2×D11)⋊C16C22semidirect
52. (C2×D11)⋊C16C22semidirect
53. #10622143C22semidirect
54. #10622142C22semidirect
55. #10622141C22semidirect
56. #10622141C22semidirect
57. #10622128C22semidirect
58. #10622127C22semidirect
208. #2184D11semidirect
478. C11#33764semidirect

Maximal subgroups

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

subgroupindex
#130782812
#130782602
#130708252
#130708042
#130708002
#130707952
#130707282
#130707162
#130707112
#130706992
#130705452
#130705362
#130702282
C11×#21842
#3376411