Finite Group Databasebeta

← #14909503

Subgroups — #14909503

Order 2816.

642 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
1D11×#467C211yesmaximal, characteristic, complemented
2D11×#466C211yesmaximal, characteristic
3#13070815C211yesmaximal, characteristic, complemented
4#13070812C211yesmaximal, characteristic, complemented
5#13070803C211yesmaximal, characteristic, complemented
6#13070800C211yesmaximal, characteristic, complemented
7#13070714C211yesmaximal, characteristic, complemented
8#13070712C211yesmaximal, characteristic, complemented
9#13070710C211yesmaximal, characteristic, complemented
10#13070546C211yesmaximal, characteristic, complemented
11#13070543C211yesmaximal, characteristic, complemented
12#13070534C211yesmaximal, characteristic, complemented
13#13070531C211yesmaximal, characteristic, complemented
14C2×(C2×D11)⋊C16C211yesmaximal, characteristic, complemented
15C11×#2217C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic, complemented
17C2×D8×D11C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19D11×C22⋊Q8—21no—
20D11×#121—21no—
21C2×C11×SD32C2211yescharacteristic, complemented
22C22×C11×C16C2211yescharacteristic, complemented
23C11×#467C2211yescharacteristic, complemented
24C11×#466C2211yescharacteristic
25#10622801C2211yescharacteristic
26C2×#66892C2211yescharacteristic, complemented
27#10622770C2211yescharacteristic
28C2×#66891C2211yescharacteristic, complemented
29#10622729C2211yescharacteristic, complemented
30#10622728C2211yescharacteristic
31C22×C11⋊C16C2211yescharacteristic, complemented
32#10622664—21no—
33#10622651—21no—
34C2×#66864C2211yescharacteristic, complemented
35#10622500C2211yescharacteristic
36#10622496C2211yescharacteristic
37D11×#107C2211yescharacteristic
38D11×#107C2211yescharacteristic, complemented
39#10622426—21no—
40D11×#103—21no—
41#10622388—21no—
42D11×#102—21no—
43C11×#367C2211yescharacteristic, complemented
44C11×#358C2211yescharacteristic, complemented
45C11×#357C2211yescharacteristic, complemented
46#10622202C2211yescharacteristic, complemented
47#10622200C2211yescharacteristic, complemented
48#10622147C2211yescharacteristic, complemented
49(C2×D11)⋊C16C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic
51(C2×D11)⋊C16C2211yescharacteristic, complemented
52(C2×D11)⋊C16C2211yescharacteristic, complemented
53#10622143C2211yescharacteristic, complemented
54#10622141C2211yescharacteristic, complemented
55#10622130C2211yescharacteristic, complemented
56#10622129C2211yescharacteristic, complemented
57#10622128C2211yescharacteristic, complemented
58#10622128C2211yescharacteristic, complemented
59C2×Q8×D11—21no—
60C2×D4×D11—21no—
61C2×D4×D11—41no—
62C22×C4×D11D411yescharacteristic
63C2×C11×Q16C2311yescharacteristic
64C2×C11×D8C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×C22⋊Q8—21no—
67C11×#121—21no—
68#66999—21no—
69C2×#4326—21no—
70#66992—41no—
71#66991—21no—
72C2×#4323—21no—
73#66983—21no—
74#66977—21no—
75C22×C11⋊C8D411yescharacteristic
76Q16×D11—41no—
77Q16×D11—41no—
78D8×D11—41no—
79D8×D11—41no—
80C2×Dic44C2311yescharacteristic
81C2×D88C2311yescharacteristic
82C2×C8×D11—41no—
83C2×C8×D11—41no—
84C2×C8×D11D411yescharacteristic
85C2×C8×D11D411yescharacteristic
86C2×C8×D11C2311yescharacteristic
87C2×C8×D11C2311yescharacteristic
88#66950—21no—
89#66949—41no—
90#66948—21no—
91C4⋊C4×D11—21no—
92C4⋊C4×D11—21no—
93C4⋊C4×D11—41no—
94#66937—41no—
95C22⋊C4×D11—41no—
96C22⋊C4×D11—41no—
97#66931—41no—
98C11×SD32—41no—
99C2×C11×C16—41no—
100C2×C11×C16C2311yescharacteristic
101C2×C11×C16C2311yescharacteristic
102C11×#107C2311yescharacteristic
103C11×#107C2311yescharacteristic
104C11×#103—21no—
105C11×#102—21no—
106#66899—21no—
107#66896—21no—
108#66892—41no—
109#66891—41no—
110#66885—21no—
111#66882C2311yescharacteristic
112#66882C2311yescharacteristic
113#66880—21no—
114C2×C11⋊C16—41no—
115C2×C11⋊C16C2311yescharacteristic
116C2×C11⋊C16C2311yescharacteristic
117#66874—21no—
118#66873—21no—
119#66871—21no—
120#66871—21no—
121#66864—41no—
122#33753—111nomaximal, Sylow
123C23×D11—41no—
124C23×D11D811yescharacteristic
125C2×Q8×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—41no—
128C22×C4×C11C2×D411yescharacteristic
129C2×C22⋊D11—41no—
130C2×C22⋊D11—41no—
131C2×C22⋊D11—41no—
132C22×Dic11D811yescharacteristic
133Q8×D11—42no—
134Q8×D11—42no—
135D4×D11—42no—
136D4×D11—42no—
137D4×D11—84no—
138C2×D44—21no—
139C2×D44—41no—
140C2×C4×D11—41no—
141C2×C4×D11—41no—
142C2×C4×D11—41no—
143C2×C4×D11—41no—
144C2×C4×D11—41no—
145C2×C4×D11D811yescharacteristic
146C2×C4×D11D811yescharacteristic
147C2×C4×D11C2×D411yescharacteristic
148C2×C4×D11C2×D411yescharacteristic
149C2×Dic22—21no—
150C2×Dic22—41no—
151C11×Q16—21no—
152C11×Q16—21no—
153C11×D8—21no—
154C11×D8—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11C2×D411yescharacteristic
158C2×C8×C11C2411yescharacteristic
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—41no—
162C11×C22⋊C4—41no—
163C11×C22⋊C4—41no—
164C22⋊Dic11—41no—
165C22⋊Dic11—41no—
166#4326—42no—
167#4323—42no—
168(C2×D11)⋊C4—41no—
169(C2×D11)⋊C4—41no—
170(C2×D11)⋊C4—41no—
171(C2×D11)⋊C4—41no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—41no—
175Dic11⋊C4—41no—
176Dic11⋊C4—41no—
177Dic11⋊C4—41no—
178Dic11⋊C4—41no—
179C2×C11⋊C8—41no—
180C2×C11⋊C8C2×D411yescharacteristic
181C2×C11⋊C8C2×D411yescharacteristic
182Dic44—21no—
183Dic44—21no—
184D88—21no—
185D88—21no—
186C8×D11—21no—
187C8×D11—21no—
188C8×D11—21no—
189C8×D11—21no—
190C8×D11—41no—
191C8×D11—41no—
192C11×C16—21no—
193C11×C16—21no—
194C11⋊C16—21no—
195C11⋊C16—21no—
196C2×#467—111no—
197C2×#466—111no—
198#2235—111no—
199#2235—111no—
200#2233—111no—
201#2233—111no—
202#2217—111no—
203#2217—111no—
204#2217—111no—
205#2217D1111yescharacteristic, complemented
206#2187—111no—
207#2187—111no—
208#2185—111no—
209#2185—111no—
210C2×C22⋊C16—111no—
211C23×C11—41no—
212C23×C11C2×D811yescharacteristic
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—82no—
217C22×D11—82no—
218C22×D11—82no—
219C22×D11SD3214yescomplemented
220C22×D11C2×D811yescharacteristic
221C22×D11C2×D811yescharacteristic
222Q8×C11—41no—
223Q8×C11—41no—
224D4×C11—41no—
225D4×C11—41no—
226D4×C11—82no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11C2×D811yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C22⋊D11—82no—
235C22⋊D11—82no—
236C22⋊D11—82no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11C2×D811yescharacteristic
242C2×Dic11C2×D811yescharacteristic
243D44—41no—
244D44—41no—
245D44—82no—
246C4×D11—21no—
247C4×D11—21no—
248C4×D11—21no—
249C4×D11—21no—
250C4×D11—41no—
251C4×D11—41no—
252C4×D11—82no—
253C4×D11—82no—
254C4×D11—82no—
255Dic22—41no—
256Dic22—41no—
257Dic22—82no—
258C8×C11—21no—
259C8×C11H(5,𝔽2)11yescharacteristic
260C8×C11H(5,𝔽2)11yescharacteristic
261C11⋊C8—21no—
262C11⋊C8—21no—
263C22×Q16—111no—
264C22×D8—111no—
265C23×C8—111no—
266C2×C22⋊Q8—221no—
267C2×#121—221no—
268C2×SD32—111no—
269C2×SD32—111no—
270C2×SD32—111no—
271C2×SD32C2×D1111yescharacteristic, complemented
272C22×C16—111no—
273C22×C16C2×D1111yescharacteristic, complemented
274#467—111no—
275#467—111no—
276#467—111no—
277#467—221no—
278#467—221no—
279#467C2×D1111yescharacteristic, complemented
280#466—111no—
281#466—111no—
282#466—111no—
283#466—221no—
284#466—221no—
285#466C2×D1111yescharacteristic
286C2×#107—111no—
287C2×#107—111no—
288C2×#103—221no—
289C2×#102—221no—
290#367—111no—
291#367—111no—
292#367—111no—
293#367C2×D1111yescharacteristic, complemented
294#358—111no—
295#358—111no—
296#358—111no—
297#358C2×D1111yescharacteristic, complemented
298#357—111no—
299#357—111no—
300#357—111no—
301#357C2×D1111yescharacteristic, complemented
302C22⋊C16—111no—
303C22⋊C16—111no—
304C22⋊C16—111no—
305C22⋊C16—111no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11C2×SD3212yes—
312C22×C11C22×D811yescharacteristic
313C2×D11—21no—
314C2×D11—21no—
315C2×D11—21no—
316C2×D11—21no—
317C2×D11—44no—
318C2×D11—81no—
319C2×D11—81no—
320C2×D11—81no—
321C2×D11—164no—
322C2×D11C2×SD3212yes—
323C2×D11C2×SD3212yes—
324C4×C11—21no—
325C4×C11—81no—
326C4×C11—81no—
327C4×C11—81no—
328C4×C11#53411yescharacteristic
329C4×C11#57511yescharacteristic
330Dic11—21no—
331Dic11—21no—
332Dic11—81no—
333Dic11—81no—
334Dic11—81no—
335C22×Q8—221no—
336C22×D4—221no—
337C22×D4—441no—
338C23×C4—111no—
339C2×Q16—111no—
340C2×Q16—221no—
341C2×Q16—441no—
342C2×Q16—441no—
343C2×Q16C22×D1111yescharacteristic
344C2×D8—111no—
345C2×D8—221no—
346C2×D8—441no—
347C2×D8—441no—
348C2×D8C22×D1111yescharacteristic
349C22×C8—111no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8—111no—
354C22×C8—441no—
355C22×C8—441no—
356C22×C8C22×D1111yescharacteristic
357C22⋊Q8—21no—
358C22⋊Q8—221no—
359C22⋊Q8—221no—
360C22⋊Q8—221no—
361C22⋊Q8—441no—
362C22⋊Q8—441no—
363#121—21no—
364#121—221no—
365#121—221no—
366#121—221no—
367#121—441no—
368#121—441no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—441no—
372C2×C22⋊C4—441no—
373C2×C22⋊C4—441no—
374SD32—41no—
375SD32—441no—
376SD32—441no—
377SD32—441no—
378C2×C16—41no—
379C2×C16—111no—
380C2×C16—111no—
381C2×C16—441no—
382C2×C16C22×D1111yescharacteristic
383C2×C16C22×D1111yescharacteristic
384#107—111no—
385#107—111no—
386#107—221no—
387#107—221no—
388#107C22×D1111yescharacteristic
389#107C22×D1111yescharacteristic
390#103—21no—
391#103—221no—
392#103—221no—
393#103—221no—
394#102—21no—
395#102—221no—
396#102—221no—
397#102—221no—
398C2×C11—22no—
399C2×C11—161no—
400C2×C11#318611yescharacteristic
401C2×C11C22×SD3211yescharacteristic
402C2×C11#341411yescharacteristic
403D11—22no—
404D11—22no—
405D11—161no—
406C24—111no—
407C24—441no—
408C2×Q8—21no—
409C2×Q8—221no—
410C2×Q8—441no—
411C2×Q8—442no—
412C2×Q8—442no—
413C2×D4—21no—
414C2×D4—41no—
415C2×D4—221no—
416C2×D4—441no—
417C2×D4—441no—
418C2×D4—442no—
419C2×D4—442no—
420C2×D4—441no—
421C2×D4—441no—
422C2×D4—884no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—441no—
429C22×C4—441no—
430C22×C4—441no—
431C22×C4—441no—
432C22×C4—441no—
433C22×C4D4×D1111yescharacteristic
434Q16—21no—
435Q16—21no—
436Q16—221no—
437Q16—221no—
438Q16—442no—
439D8—21no—
440D8—21no—
441D8—221no—
442D8—221no—
443D8—442no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—111no—
447C2×C8—111no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—441no—
453C2×C8—441no—
454C2×C8—441no—
455C2×C8D4×D1111yescharacteristic
456C2×C8C23×D1111yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—441no—
463C4⋊C4—441no—
464C4⋊C4—441no—
465C4⋊C4—441no—
466C4⋊C4—441no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C22⋊C4—441no—
470C22⋊C4—441no—
471C22⋊C4—441no—
472C22⋊C4—441no—
473C22⋊C4—441no—
474C22⋊C4—441no—
475C16—21no—
476C16—21no—
477C16—221no—
478C16—221no—
479C11#3375311yescharacteristic, complemented, Sylow
480C23—41no—
481C23—111no—
482C23—111no—
483C23—114no—
484C23—441no—
485C23—441no—
486C23—441no—
487C23—882no—
488C23—882no—
489C23—882no—
490C23D8×D1111yescharacteristic
491Q8—41no—
492Q8—41no—
493Q8—441no—
494Q8—441no—
495Q8—882no—
496D4—41no—
497D4—41no—
498D4—82no—
499D4—441no—
500D4—441no—
501D4—882no—
502D4—882no—
503D4—882no—
504D4—882no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—111no—
511C2×C4—111no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—882no—
523C2×C4—882no—
524C2×C4—882no—
525C2×C4D8×D1111yescharacteristic
526C2×C4C2×D4×D1111yescharacteristic
527C8—21no—
528C8—221no—
529C8—221no—
530C8#6703711yescharacteristic
531C8#6704211yescharacteristic
532C22—21no—
533C22—21no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—112no—
538C22—112no—
539C22—221no—
540C22—221no—
541C22—221no—
542C22—221no—
543C22—444no—
544C22—881no—
545C22—881no—
546C22—881no—
547C22—1764no—
548C22D11×SD3212yes—
549C22C2×D8×D1111yescharacteristic
550C4—21no—
551C4—81no—
552C4—81no—
553C4—81no—
554C4—221no—
555C4—221no—
556C4—881no—
557C4—881no—
558C4—881no—
559C4#1062313611yescharacteristic
560C4#1062329911yescharacteristic
561C2—22no—
562C2—161no—
563C2—222no—
564C2—222no—
565C2—1761no—
566C2#1307936311yescharacteristic
567C2C2×D11×SD3211yescharacteristic
568C2#1308174911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2217C2
socleC22×C11C22×D8
prime radicalD11×#466C2
hypercenter#2217D11
hypocenterC11#33753
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. D11×#467C2semidirect
3. #13070815C2semidirect
4. #13070812C2semidirect
5. #13070803C2semidirect
6. #13070800C2semidirect
7. #13070714C2semidirect
8. #13070712C2semidirect
9. #13070710C2semidirect
10. #13070546C2semidirect
11. #13070543C2semidirect
12. #13070534C2semidirect
13. #13070531C2semidirect
14. C2×(C2×D11)⋊C16C2semidirect
15. C11×#2217C2semidirect
16. C2×Q16×D11C22semidirect
21. C2×C11×SD32C22semidirect
22. C22×C11×C16C22semidirect
23. C11×#467C22semidirect
26. C2×#66892C22semidirect
28. C2×#66891C22semidirect
29. #10622729C22semidirect
31. C22×C11⋊C16C22semidirect
34. C2×#66864C22semidirect
38. D11×#107C22semidirect
43. C11×#367C22semidirect
44. C11×#358C22semidirect
45. C11×#357C22semidirect
46. #10622202C22semidirect
47. #10622200C22semidirect
48. #10622147C22semidirect
51. (C2×D11)⋊C16C22semidirect
52. (C2×D11)⋊C16C22semidirect
53. #10622143C22semidirect
54. #10622141C22semidirect
55. #10622130C22semidirect
56. #10622129C22semidirect
57. #10622128C22semidirect
58. #10622128C22semidirect
205. #2217D11semidirect
219. C22×D11SD32semidirect
271. C2×SD32C2×D11semidirect
273. C22×C16C2×D11semidirect
279. #467C2×D11semidirect
293. #367C2×D11semidirect
297. #358C2×D11semidirect
301. #357C2×D11semidirect
479. C11#33753semidirect

Maximal subgroups

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

subgroupindex
D11×#4672
D11×#4662
#130708152
#130708122
#130708032
#130708002
#130707142
#130707122
#130707102
#130705462
#130705432
#130705342
#130705312
C2×(C2×D11)⋊C162
C11×#22172
#3375311