Finite Group Databasebeta

← #14909605

Subgroups — #14909605

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#13078286C211yesmaximal, characteristic, complemented
2#13078264C211yesmaximal, characteristic, complemented
3#13070825C211yesmaximal, characteristic, complemented
4#13070808C211yesmaximal, characteristic, complemented
5#13070802C211yesmaximal, characteristic, complemented
6#13070797C211yesmaximal, characteristic, complemented
7#13070729C211yesmaximal, characteristic, complemented
8#13070719C211yesmaximal, characteristic, complemented
9#13070712C211yesmaximal, characteristic, complemented
10#13070702C211yesmaximal, characteristic, complemented
11#13070547C211yesmaximal, characteristic, complemented
12#13070541C211yesmaximal, characteristic, complemented
13#13070541C211yesmaximal, characteristic, complemented
14#13070530C211yesmaximal, characteristic, complemented
15C11×#2113C211yesmaximal, characteristic, complemented
16C2×C11×#131C2211yescharacteristic
17#10623364—21no—
18#10623361—21no—
19C2×#66957C2211yescharacteristic, complemented
20C22×D88C2211yescharacteristic
21C2×C11×M32C2211yescharacteristic, complemented
22C22×C11×C16C2211yescharacteristic, complemented
23#10622748—21no—
24#10622748—21no—
25#10622747—21no—
26#10622747—21no—
27#10622746—21no—
28#10622744—21no—
29#10622729C2211yescharacteristic
30#10622729C2211yescharacteristic, complemented
31#10622728C2211yescharacteristic
32#10622728C2211yescharacteristic
33#10622728C2211yescharacteristic
34#10622728C2211yescharacteristic
35#10622728C2211yescharacteristic
36#10622728C2211yescharacteristic, complemented
37#10622719C2211yescharacteristic
38C2×#66882C2211yescharacteristic, complemented
39C2×#66864C2211yescharacteristic
40C2×#66864C2211yescharacteristic
41C2×D176C2211yescharacteristic
42C2×D176C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic
45C11×C22⋊C16C2211yescharacteristic, complemented
46C11×C22⋊C16C2211yescharacteristic, complemented
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622147C2211yescharacteristic, complemented
52#10622147C2211yescharacteristic, complemented
53#10622143C2211yescharacteristic, complemented
54#10622143C2211yescharacteristic, complemented
55#10622142C2211yescharacteristic, complemented
56#10622142C2211yescharacteristic, complemented
57#10622141C2211yescharacteristic, complemented
58#10622141C2211yescharacteristic, complemented
59C2×C11×#41D411yescharacteristic
60C2×#4339—21no—
61C22×D44—21no—
62C11×#131—41no—
63C11×#131—41no—
64C2×C11×M16D411yescharacteristic
65C2×C11×M16D411yescharacteristic
66C2×C11×M16D411yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70#67000—41no—
71#66999—41no—
72#66993—41no—
73#66992—41no—
74#66992—41no—
75#66991—41no—
76#66990—41no—
77#66990—41no—
78#66983—21no—
79#66983—21no—
80#66983—21no—
81#66983—21no—
82#66983—21no—
83#66983—21no—
84#66979—21no—
85C2×C4⋊Dic11—21no—
86#66977—21no—
87#66977—21no—
88C2×Dic44C2311yescharacteristic
89#66957—41no—
90#66957—41no—
91C2×D88—21no—
92C2×D88—41no—
93C2×D88—41no—
94C2×D88C2311yescharacteristic
95C2×D88C2311yescharacteristic
96C2×D88C2311yescharacteristic
97C2×#4314—21no—
98C11×M32—41no—
99C2×C11×C16—41no—
100C2×C11×C16C2311yescharacteristic
101C2×C11×C16C2311yescharacteristic
102C2×C11×C16C2311yescharacteristic
103C2×C11×C16C2311yescharacteristic
104#66885—21no—
105#66885—21no—
106#66885—21no—
107#66885—21no—
108#66885—21no—
109#66885—21no—
110#66882—21no—
111#66882C2311yescharacteristic
112#66882C2311yescharacteristic
113#66882C2311yescharacteristic
114#66882C2311yescharacteristic
115#66881—21no—
116#66880—21no—
117#66880—21no—
118#66864—41no—
119#66864—41no—
120D176—41no—
121D176—41no—
122#33764—111nomaximal, Sylow
123C23×D11—41no—
124C11×#41—41no—
125C11×#41—41no—
126C2×Q8×C11D811yescharacteristic
127C2×D4×C11D811yescharacteristic
128C2×D4×C11D811yescharacteristic
129C2×D4×C11D811yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C2×C22⋊D11—41no—
134C2×C22⋊D11—41no—
135C2×C22⋊D11—41no—
136C2×C22⋊D11—41no—
137C2×C22⋊D11—41no—
138C2×C22⋊D11—41no—
139C2×C22⋊D11—41no—
140C22×Dic11—41no—
141#4339—42no—
142#4339—42no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—42no—
147C2×D44—42no—
148C2×D44—41no—
149C2×C4×D11—41no—
150C2×Dic22—21no—
151C11×M16—41no—
152C11×M16—41no—
153C11×M16—41no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11C2×D411yescharacteristic
161C2×C8×C11C2×D411yescharacteristic
162C2×C8×C11C2×D411yescharacteristic
163C2×C8×C11C2411yescharacteristic
164C22⋊Dic11—41no—
165C22⋊Dic11—41no—
166C22⋊Dic11—41no—
167(C2×D11)⋊C4—41no—
168(C2×D11)⋊C4—41no—
169(C2×D11)⋊C4—41no—
170(C2×D11)⋊C4—41no—
171(C2×D11)⋊C4—41no—
172(C2×D11)⋊C4—41no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—41no—
178Dic11⋊C4—41no—
179Dic11⋊C4—41no—
180C4×Dic11—41no—
181Dic44—21no—
182Dic44—21no—
183D88—21no—
184D88—21no—
185D88—21no—
186D88—21no—
187D88—21no—
188D88—21no—
189D88—42no—
190#4314—42no—
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#2184—111no—
209#2113D1111yescharacteristic, complemented
210C23×C11C2×D811yescharacteristic
211C23×C11C2×D811yescharacteristic
212C23×C11C2×D811yescharacteristic
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—82no—
217C22×D11—161no—
218C22×D11—161no—
219Q8×C11—41no—
220D4×C11—41no—
221D4×C11—41no—
222D4×C11—41no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11C2×D811yescharacteristic
230C2×C4×C11C2×D811yescharacteristic
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—
239C22⋊D11—161no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—161no—
246D44—41no—
247D44—41no—
248D44—41no—
249D44—41no—
250D44—41no—
251D44—41no—
252D44—82no—
253C4×D11—82no—
254Dic22—41no—
255Dic22—41no—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11H(5,𝔽2)11yescharacteristic
260C8×C11H(5,𝔽2)11yescharacteristic
261C2×#135—111no—
262C22×D8—111no—
263C2×#131C2×D1111yescharacteristic
264#537—221no—
265#535—221no—
266C2×SD32—111no—
267C2×SD32—111no—
268C2×D16—111no—
269C2×D16—111no—
270C2×M32C2×D1111yescharacteristic, complemented
271C22×C16C2×D1111yescharacteristic, complemented
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#466—111no—
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#357—111no—
299#357—111no—
300C22⋊C16C2×D1111yescharacteristic
301C22⋊C16C2×D1111yescharacteristic
302C22⋊C16C2×D1111yescharacteristic, complemented
303C22⋊C16C2×D1111yescharacteristic, complemented
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×C11C22×D811yescharacteristic
314C2×D11—81no—
315C2×D11—81no—
316C2×D11—81no—
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#53411yescharacteristic
328C4×C11#57511yescharacteristic
329Dic11—81no—
330Dic11—81no—
331Dic11—81no—
332Dic11—81no—
333Dic11—81no—
334C2×#41—221no—
335C2×#41D4411yescharacteristic
336C22×D4—221no—
337#135—441no—
338#135—441no—
339C2×Q16—111no—
340C2×SD16—221no—
341C2×D8—111no—
342C2×D8—111no—
343C2×D8—111no—
344C2×D8—221no—
345C2×D8—441no—
346C2×D8—441no—
347#131—41no—
348#131—41no—
349C2×M16D4411yescharacteristic
350C2×M16D4411yescharacteristic
351C2×M16D4411yescharacteristic
352C22×C8C22×D1111yescharacteristic
353C22×C8C22×D1111yescharacteristic
354C22×C8C22×D1111yescharacteristic
355#127—441no—
356#124—441no—
357C22⋊Q8—221no—
358C22⋊Q8—221no—
359C22⋊Q8—441no—
360#121—221no—
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—441no—
376D16—441no—
377M32—41no—
378C2×C16—41no—
379C2×C16C22×D1111yescharacteristic
380C2×C16C22×D1111yescharacteristic
381C2×C16C22×D1111yescharacteristic
382C2×C16C22×D1111yescharacteristic
383#107—111no—
384#107—111no—
385#107—111no—
386#107—111no—
387#107—221no—
388#106—221no—
389#103—221no—
390#103—221no—
391#102—221no—
392#102—221no—
393#102—221no—
394#102—221no—
395#102—221no—
396#102—221no—
397C2×C11—41no—
398C2×C11—41no—
399C2×C11—41no—
400C2×C11#318611yescharacteristic
401C2×C11#341511yescharacteristic
402C2×C11#341611yescharacteristic
403D11—161no—
404D11—161no—
405D11—161no—
406C24—441no—
407#41—41no—
408#41—41no—
409#41—442no—
410#41—442no—
411C2×Q8—221no—
412C2×Q8D8811yescharacteristic
413C2×D4—221no—
414C2×D4—221no—
415C2×D4—221no—
416C2×D4—442no—
417C2×D4—442no—
418C2×D4—441no—
419C2×D4—441no—
420C2×D4—441no—
421C2×D4—441no—
422C2×D4—441no—
423C2×D4—441no—
424C2×D4—441no—
425C2×D4—441no—
426C2×D4D8811yescharacteristic
427C2×D4D8811yescharacteristic
428C2×D4D8811yescharacteristic
429C22×C4—441no—
430C22×C4—441no—
431C22×C4C2×D4411yescharacteristic
432C22×C4C2×D4411yescharacteristic
433C22×C4C2×D4411yescharacteristic
434Q16—221no—
435Q16—221no—
436SD16—442no—
437D8—221no—
438D8—221no—
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×D4411yescharacteristic
454C2×C8C2×D4411yescharacteristic
455C2×C8C2×D4411yescharacteristic
456C2×C8C23×D1111yescharacteristic
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—441no—
462C4⋊C4—441no—
463C4⋊C4—441no—
464C22⋊C4—441no—
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—21no—
477C16—21no—
478C11#3376411yescharacteristic, complemented, Sylow
479C23—441no—
480C23—441no—
481C23—441no—
482C23—882no—
483C23—1761no—
484C23—1761no—
485C23C2×D8811yescharacteristic
486C23C2×D8811yescharacteristic
487C23C2×D8811yescharacteristic
488Q8—41no—
489Q8—441no—
490Q8—441no—
491D4—41no—
492D4—41no—
493D4—41no—
494D4—441no—
495D4—441no—
496D4—441no—
497D4—441no—
498D4—441no—
499D4—441no—
500D4—882no—
501D4—882no—
502D4—1761no—
503D4—1761no—
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—441no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—882no—
520C2×C4—1761no—
521C2×C4C2×D8811yescharacteristic
522C2×C4C2×D8811yescharacteristic
523C2×C4C2×D8811yescharacteristic
524C2×C4C22×D4411yescharacteristic
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—881no—
540C22—881no—
541C22—881no—
542C22—881no—
543C22—881no—
544C22—881no—
545C22—881no—
546C22—881no—
547C22—881no—
548C22—1764no—
549C22C22×D8811yescharacteristic
550C4—21no—
551C4—21no—
552C4—21no—
553C4—881no—
554C4—881no—
555C4—881no—
556C4—881no—
557C4—881no—
558C4#1062302411yescharacteristic
559C4#1062327911yescharacteristic
560C2—41no—
561C2—41no—
562C2—41no—
563C2—1761no—
564C2—1761no—
565C2—1761no—
566C2#1307936711yescharacteristic
567C2#1308175711yescharacteristic
568C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2113C2
socleC22×C11C22×D8
hypercenter#2113D11
hypocenterC11#33764
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #2113

Complements

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

NH ≅ G/Ntype
1. #13078286C2semidirect
2. #13078264C2semidirect
3. #13070825C2semidirect
4. #13070808C2semidirect
5. #13070802C2semidirect
6. #13070797C2semidirect
7. #13070729C2semidirect
8. #13070719C2semidirect
9. #13070712C2semidirect
10. #13070702C2semidirect
11. #13070547C2semidirect
12. #13070541C2semidirect
13. #13070541C2semidirect
14. #13070530C2semidirect
15. C11×#2113C2semidirect
19. C2×#66957C22semidirect
21. C2×C11×M32C22semidirect
22. C22×C11×C16C22semidirect
30. #10622729C22semidirect
36. #10622728C22semidirect
38. C2×#66882C22semidirect
45. C11×C22⋊C16C22semidirect
46. C11×C22⋊C16C22semidirect
51. #10622147C22semidirect
52. #10622147C22semidirect
53. #10622143C22semidirect
54. #10622143C22semidirect
55. #10622142C22semidirect
56. #10622142C22semidirect
57. #10622141C22semidirect
58. #10622141C22semidirect
209. #2113D11semidirect
270. C2×M32C2×D11semidirect
271. C22×C16C2×D11semidirect
302. C22⋊C16C2×D11semidirect
303. C22⋊C16C2×D11semidirect
478. C11#33764semidirect

Maximal subgroups

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

subgroupindex
#130782862
#130782642
#130708252
#130708082
#130708022
#130707972
#130707292
#130707192
#130707122
#130707022
#130705472
#130705412
#130705302
C11×#21132
#3376411