Finite Group Databasebeta

← SD32×C22⋊D11 #14910441

Subgroups — SD32×C22⋊D11 #14910441

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×SD32C211yesmaximal, characteristic, complemented
2Q16×C22⋊D11C211yesmaximal, characteristic, complemented
3D8×C22⋊D11C211yesmaximal, characteristic
4#13070870C211yesmaximal, characteristic, complemented
5#13070712C211yesmaximal, characteristic, complemented
6#13070709C211yesmaximal, characteristic, complemented
7#13070659C211yesmaximal, characteristic, complemented
8#13070654C211yesmaximal, characteristic, complemented
9#13070545C211yesmaximal, characteristic, complemented
10#13070543C211yesmaximal, characteristic, complemented
11#13070533C211yesmaximal, characteristic, complemented
12#13070531C211yesmaximal, characteristic, complemented
13SD32×Dic11C211yesmaximal, characteristic, complemented
14C16×C22⋊D11C211yesmaximal, characteristic, complemented
15C22×C11×SD32C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic, complemented
17C22×C11×D8C2211yescharacteristic
18Q8×C22⋊D11—21no—
19D4×C22⋊D11—21no—
20C2×Q16×D11C2211yescharacteristic, complemented
21C2×D8×D11C2211yescharacteristic
22C2×C11×SD32—24no—
23C2×C11×SD32C2211yescharacteristic
24C2×C11×SD32C2211yescharacteristic
25C2×C11×SD32C2211yescharacteristic, complemented
26C2×C11×SD32C2211yescharacteristic, complemented
27C22×C11×C16C2211yescharacteristic, complemented
28#10622841—21no—
29#10622830—21no—
30#10622801C2211yescharacteristic, complemented
31#10622799—21no—
32Q16×Dic11C2211yescharacteristic, complemented
33#10622795—21no—
34#10622794C2211yescharacteristic, complemented
35C2×#66892C2211yescharacteristic, complemented
36C2×#66892C2211yescharacteristic, complemented
37#10622770C2211yescharacteristic
38#10622769—21no—
39#10622764C2211yescharacteristic
40#10622763—21no—
41D8×Dic11C2211yescharacteristic
42C2×#66891C2211yescharacteristic
43C2×#66891C2211yescharacteristic, complemented
44#10622729C2211yescharacteristic, complemented
45#10622728C2211yescharacteristic
46C8×C22⋊D11C2211yescharacteristic
47D11×SD32—24no—
48C2×#66864C2211yescharacteristic, complemented
49C2×C16×D11C2211yescharacteristic, complemented
50#10622202C2211yescharacteristic, complemented
51#10622202C2211yescharacteristic, complemented
52#10622200C2211yescharacteristic
53#10622200C2211yescharacteristic, complemented
54C22⋊(C11⋊C16)C2211yescharacteristic, complemented
55#10622147C2211yescharacteristic, complemented
56(C2×D11)⋊C16C2211yescharacteristic, complemented
57#10622143C2211yescharacteristic, complemented
58#10622141C2211yescharacteristic, complemented
59Dic11⋊C16C2211yescharacteristic, complemented
60C16×Dic11C2211yescharacteristic, complemented
61C22×Q8×C11—21no—
62C22×D4×C11—21no—
63C22×C22⋊D11—41no—
64C2×Q8×D11—21no—
65C2×D4×D11—21no—
66C2×C11×Q16—22no—
67C2×C11×Q16—21no—
68C2×C11×Q16—41no—
69C2×C11×Q16C2311yescharacteristic
70C2×C11×Q16C2311yescharacteristic
71C2×C11×D8—22no—
72C2×C11×D8—21no—
73C2×C11×D8—41no—
74C2×C11×D8C2311yescharacteristic
75C2×C11×D8C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77#67006—41no—
78#66999—21no—
79#66999—41no—
80Q8×Dic11—21no—
81#66997—21no—
82#66997—41no—
83C2×#4326—21no—
84C2×#4326—21no—
85#66993—21no—
86#66992—41no—
87#66991—21no—
88#66990—41no—
89D4×Dic11—21no—
90C2×#4323—21no—
91C2×#4323—21no—
92#66983—21no—
93C4×C22⋊D11—41no—
94C4×C22⋊D11D411yescharacteristic
95#66977—21no—
96#66977—41no—
97Q16×D11—22no—
98Q16×D11—41no—
99D8×D11—22no—
100D8×D11—41no—
101C2×Dic44C2311yescharacteristic
102C2×D88C2311yescharacteristic
103C2×C8×D11C2311yescharacteristic
104C11×SD32—22no—
105C11×SD32—22no—
106C11×SD32—22no—
107C11×SD32D414yescomplemented
108C2×C11×C16—22no—
109C2×C11×C16C2311yescharacteristic
110C2×C11×C16C2311yescharacteristic
111#66899—21no—
112#66899—21no—
113#66896—21no—
114#66896—21no—
115C22⋊(C11⋊C8)D411yescharacteristic
116#66892—22no—
117#66892—41no—
118#66891—22no—
119#66891—41no—
120#66885—21no—
121(C2×D11)⋊C8D411yescharacteristic
122#66882C2311yescharacteristic
123#66882C2311yescharacteristic
124#66880—21no—
125Dic11⋊C8D411yescharacteristic
126C8×Dic11C2311yescharacteristic
127C2×C11⋊C16C2311yescharacteristic
128C2×C11⋊C16C2311yescharacteristic
129#66864—22no—
130C16×D11—22no—
131D4×SD32—111nomaximal, Sylow
132C24×C11—41no—
133C23×D11—41no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—42no—
137C2×Q8×C11—41no—
138C2×Q8×C11—81no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—42no—
142C2×D4×C11—41no—
143C2×D4×C11—81no—
144C22×C4×C11—41no—
145C22×C4×C11C2×D411yescharacteristic
146C2×C22⋊D11—41no—
147C2×C22⋊D11—41no—
148C2×C22⋊D11—41no—
149C2×C22⋊D11—41no—
150C2×C22⋊D11—41no—
151C2×C22⋊D11—84no—
152C2×C22⋊D11D811yescharacteristic
153C22×Dic11—41no—
154Q8×D11—42no—
155Q8×D11—81no—
156D4×D11—42no—
157D4×D11—81no—
158C2×D44—21no—
159C2×C4×D11—41no—
160C2×C4×D11C2×D411yescharacteristic
161C2×Dic22—21no—
162C2×Dic22—41no—
163C11×Q16—21no—
164C11×Q16—21no—
165C11×Q16—21no—
166C11×Q16—42no—
167C11×Q16C2×D412yescomplemented
168C11×D8—21no—
169C11×D8—21no—
170C11×D8—21no—
171C11×D8—42no—
172C11×D8C2×D412yes—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2411yescharacteristic
177C22⋊Dic11—41no—
178C22⋊Dic11—41no—
179C22⋊Dic11—41no—
180C22⋊Dic11D811yescharacteristic
181#4326—42no—
182#4326—81no—
183#4323—42no—
184#4323—81no—
185(C2×D11)⋊C4—41no—
186(C2×D11)⋊C4—41no—
187(C2×D11)⋊C4D811yescharacteristic
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—41no—
191Dic11⋊C4—41no—
192Dic11⋊C4—41no—
193Dic11⋊C4—41no—
194Dic11⋊C4—41no—
195Dic11⋊C4D811yescharacteristic
196C4×Dic11—41no—
197C4×Dic11C2×D411yescharacteristic
198C2×C11⋊C8C2×D411yescharacteristic
199C2×C11⋊C8C2×D411yescharacteristic
200Dic44—21no—
201Dic44—21no—
202D88—21no—
203D88—21no—
204C8×D11—21no—
205C8×D11—21no—
206C11×C16—21no—
207C11×C16C2×D412yescomplemented
208C11⋊C16—21no—
209C11⋊C16—21no—
210C22×SD32—111no—
211C22×SD32D1111yescharacteristic, complemented
212D4×Q16—111no—
213D4×D8—111no—
214#2248—111no—
215#2217—111no—
216#2217—111no—
217#2208—111no—
218#2207—111no—
219#2187—111no—
220#2187—111no—
221#2185—111no—
222#2185—111no—
223C4×SD32—111no—
224D4×C16—111no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—82no—
228C23×C11—82no—
229C23×C11—161no—
230C23×C11C2×D811yescharacteristic
231C22×D11—41no—
232C22×D11—82no—
233C22×D11—82no—
234C22×D11—161no—
235C22×D11C2×D811yescharacteristic
236Q8×C11—22no—
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—82no—
241D4×C11—22no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—82no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—82no—
251C2×C4×C11C2×D811yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C22⋊D11—82no—
254C22⋊D11—82no—
255C22⋊D11—82no—
256C22⋊D11—82no—
257C22⋊D11—161no—
258C22⋊D11SD3214yesdirect product factor
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—82no—
263C2×Dic11C2×D811yescharacteristic
264C2×Dic11C2×D811yescharacteristic
265C2×Dic11C2×D811yescharacteristic
266D44—41no—
267D44—41no—
268C4×D11—21no—
269C4×D11—21no—
270C4×D11—82no—
271Dic22—41no—
272Dic22—41no—
273Dic22—82no—
274C8×C11—21no—
275C8×C11C22×D411yescharacteristic
276C8×C11H(5,𝔽2)11yescharacteristic
277C11⋊C8—21no—
278C11⋊C8—21no—
279C22×Q16—111no—
280C22×Q16C2×D1111yescharacteristic, complemented
281C22×D8—111no—
282C22×D8C2×D1111yescharacteristic
283D4×Q8—221no—
284D42—221no—
285C2×SD32—24no—
286C2×SD32—111no—
287C2×SD32—111no—
288C2×SD32—111no—
289C2×SD32—111no—
290C2×SD32—111no—
291C2×SD32—224no—
292C2×SD32C2×D1111yescharacteristic
293C2×SD32C2×D1111yescharacteristic
294C2×SD32C2×D1111yescharacteristic, complemented
295C2×SD32C2×D1111yescharacteristic, complemented
296C22×C16—111no—
297C22×C16C2×D1111yescharacteristic, complemented
298#494—111no—
299#493—111no—
300#467—111no—
301#467—111no—
302#466—111no—
303#466—111no—
304#462—221no—
305#459—221no—
306#451—221no—
307#451—221no—
308#447—221no—
309#447—221no—
310C4×Q16—111no—
311C4×D8—111no—
312C8×D4—111no—
313#367—111no—
314C4⋊C16—111no—
315#358—111no—
316#358—111no—
317#358—111no—
318#357—111no—
319#357—111no—
320#357—111no—
321C22⋊C16—111no—
322C22⋊C16—111no—
323C4×C16—111no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—42no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11—164no—
333C22×C11C2×SD3212yescomplemented
334C22×C11C22×D811yescharacteristic
335C2×D11—21no—
336C2×D11—21no—
337C2×D11—81no—
338C2×D11—81no—
339C2×D11—81no—
340C2×D11—164no—
341C2×D11C2×SD3212yescomplemented
342C4×C11—21no—
343C4×C11—42no—
344C4×C11—81no—
345C4×C11D4211yescharacteristic
346C4×C11#57611yescharacteristic
347Dic11—21no—
348Dic11—21no—
349Dic11—81no—
350Dic11—81no—
351Dic11—81no—
352Dic11C2×SD3212yescomplemented
353C22×Q8—21no—
354C22×Q8—221no—
355C22×D4—21no—
356C22×D4—221no—
357C22×D4—441no—
358C2×Q16—22no—
359C2×Q16—21no—
360C2×Q16—41no—
361C2×Q16—111no—
362C2×Q16—221no—
363C2×Q16—221no—
364C2×Q16—222no—
365C2×Q16—441no—
366C2×Q16C22×D1111yescharacteristic
367C2×Q16C22×D1111yescharacteristic
368C2×D8—22no—
369C2×D8—21no—
370C2×D8—41no—
371C2×D8—111no—
372C2×D8—221no—
373C2×D8—221no—
374C2×D8—222no—
375C2×D8—441no—
376C2×D8C22×D1111yescharacteristic
377C2×D8C22×D1111yescharacteristic
378C22×C8—111no—
379C22×C8C22×D1111yescharacteristic
380C4⋊Q8—221no—
381C4⋊Q8—441no—
382#127—221no—
383C22⋊Q8—221no—
384C22⋊Q8—221no—
385C22⋊Q8—441no—
386C22⋊Q8—441no—
387#121—221no—
388#121—221no—
389#121—441no—
390#120—441no—
391#120—441no—
392C4×Q8—221no—
393C4×D4—111no—
394C4×D4—221no—
395C4×D4—441no—
396SD32—22no—
397SD32—22no—
398SD32—22no—
399SD32—222no—
400SD32—222no—
401SD32—222no—
402SD32—441no—
403SD32—441no—
404SD32C22⋊D1114yesdirect product factor
405C2×C16—22no—
406C2×C16—111no—
407C2×C16—111no—
408C2×C16—222no—
409C2×C16C22×D1111yescharacteristic
410C2×C16C22×D1111yescharacteristic
411#107—111no—
412#107—111no—
413C4⋊C8—111no—
414#103—221no—
415#103—221no—
416#103—221no—
417#102—221no—
418#102—221no—
419#102—221no—
420C22⋊C8—111no—
421C22⋊C8—111no—
422C4×C8—111no—
423C2×C11—22no—
424C2×C11—82no—
425C2×C11—161no—
426C2×C11D4×D811yescharacteristic
427C2×C11C22×SD3211yescharacteristic
428C2×C11#341611yescharacteristic
429D11—22no—
430D11—161no—
431C24—41no—
432C24—441no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—42no—
436C2×Q8—41no—
437C2×Q8—81no—
438C2×Q8—221no—
439C2×Q8—441no—
440C2×Q8—442no—
441C2×Q8—881no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—42no—
445C2×D4—41no—
446C2×D4—81no—
447C2×D4—111no—
448C2×D4—221no—
449C2×D4—441no—
450C2×D4—441no—
451C2×D4—441no—
452C2×D4—442no—
453C2×D4—441no—
454C2×D4—441no—
455C2×D4—881no—
456C2×D4—884no—
457C22×C4—41no—
458C22×C4—111no—
459C22×C4—441no—
460C22×C4—441no—
461C22×C4D4×D1111yescharacteristic
462Q16—21no—
463Q16—21no—
464Q16—21no—
465Q16—42no—
466Q16—221no—
467Q16—221no—
468Q16—442no—
469Q16—881no—
470Q16C2×C22⋊D1112yescomplemented
471D8—21no—
472D8—21no—
473D8—21no—
474D8—42no—
475D8—221no—
476D8—221no—
477D8—442no—
478D8—881no—
479D8C2×C22⋊D1112yes—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8D4×D1111yescharacteristic
487C2×C8C23×D1111yescharacteristic
488C4⋊C4—111no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—441no—
492C4⋊C4—441no—
493C4⋊C4—441no—
494C4⋊C4—441no—
495C4⋊C4—441no—
496C22⋊C4—111no—
497C22⋊C4—111no—
498C22⋊C4—441no—
499C22⋊C4—441no—
500C22⋊C4—441no—
501C22⋊C4—441no—
502C22⋊C4—441no—
503C42—111no—
504C42—441no—
505C16—21no—
506C16—221no—
507C16—221no—
508C16C2×C22⋊D1112yescomplemented
509C11D4×SD3211yescharacteristic, complemented, Sylow
510C23—41no—
511C23—41no—
512C23—82no—
513C23—82no—
514C23—111no—
515C23—161no—
516C23—441no—
517C23—882no—
518C23—882no—
519C23—1761no—
520C23D8×D1111yescharacteristic
521Q8—22no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—82no—
526Q8—441no—
527Q8—441no—
528Q8—882no—
529D4—22no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—82no—
534D4—114no—
535D4—441no—
536D4—441no—
537D4—882no—
538D4—882no—
539D4—882no—
540D4—882no—
541D4—1761no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—82no—
547C2×C4—111no—
548C2×C4—111no—
549C2×C4—111no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—882no—
556C2×C4—882no—
557C2×C4D8×D1111yescharacteristic
558C2×C4C2×D4×D1111yescharacteristic
559C8—21no—
560C8—221no—
561C8—221no—
562C8#6703711yescharacteristic
563C8C22×C22⋊D1111yescharacteristic
564C22—21no—
565C22—21no—
566C22—42no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—112no—
573C22—164no—
574C22—221no—
575C22—221no—
576C22—881no—
577C22—881no—
578C22—881no—
579C22—1764no—
580C22D11×SD3212yescomplemented
581C22C2×D8×D1111yescharacteristic
582C4—21no—
583C4—42no—
584C4—81no—
585C4—112no—
586C4—221no—
587C4—221no—
588C4—881no—
589C4—881no—
590C4—881no—
591C4#1062328811yescharacteristic
592C4D4×C22⋊D1111yescharacteristic
593C2—22no—
594C2—82no—
595C2—161no—
596C2—222no—
597C2—1761no—
598C2D8×C22⋊D1111yescharacteristic
599C2C2×D11×SD3211yescharacteristic
600C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC22×C11×SD32C2
socleC22×C11C22×D8
prime radicalD8×C22⋊D11C2
hypercenterC22×SD32D11
hypocenterC11D4×SD32
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×SD32

Complements

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

NH ≅ G/Ntype
1. C2×D11×SD32C2semidirect
2. Q16×C22⋊D11C2semidirect
4. #13070870C2semidirect
5. #13070712C2semidirect
6. #13070709C2semidirect
7. #13070659C2semidirect
8. #13070654C2semidirect
9. #13070545C2semidirect
10. #13070543C2semidirect
11. #13070533C2semidirect
12. #13070531C2semidirect
13. SD32×Dic11C2semidirect
14. C16×C22⋊D11C2semidirect
15. C22×C11×SD32C2semidirect
16. C22×C11×Q16C22semidirect
20. C2×Q16×D11C22semidirect
25. C2×C11×SD32C22semidirect
26. C2×C11×SD32C22semidirect
27. C22×C11×C16C22semidirect
30. #10622801C22semidirect
32. Q16×Dic11C22semidirect
34. #10622794C22semidirect
35. C2×#66892C22semidirect
36. C2×#66892C22semidirect
43. C2×#66891C22semidirect
44. #10622729C22semidirect
48. C2×#66864C22semidirect
49. C2×C16×D11C22semidirect
50. #10622202C22semidirect
51. #10622202C22semidirect
53. #10622200C22semidirect
54. C22⋊(C11⋊C16)C22semidirect
55. #10622147C22semidirect
56. (C2×D11)⋊C16C22semidirect
57. #10622143C22semidirect
58. #10622141C22semidirect
59. Dic11⋊C16C22semidirect
60. C16×Dic11C22semidirect
107. C11×SD32D4semidirect
167. C11×Q16C2×D4semidirect
207. C11×C16C2×D4semidirect
211. C22×SD32D11semidirect
258. C22⋊D11SD32direct (N × H)
280. C22×Q16C2×D11semidirect
294. C2×SD32C2×D11semidirect
295. C2×SD32C2×D11semidirect
297. C22×C16C2×D11semidirect
333. C22×C11C2×SD32semidirect
341. C2×D11C2×SD32semidirect
352. Dic11C2×SD32semidirect
404. SD32C22⋊D11direct (N × H)
470. Q16C2×C22⋊D11semidirect
508. C16C2×C22⋊D11semidirect
509. C11D4×SD32semidirect
580. C22D11×SD32semidirect

Maximal subgroups

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

subgroupindex
C2×D11×SD322
Q16×C22⋊D112
D8×C22⋊D112
#130708702
#130707122
#130707092
#130706592
#130706542
#130705452
#130705432
#130705332
#130705312
SD32×Dic112
C16×C22⋊D112
C22×C11×SD322
D4×SD3211