Finite Group Databasebeta

← SD16×#11745659 #28560122

Subgroups — SD16×#11745659 #28560122

Order 15104.

716 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#11745659C211yesmaximal, characteristic, complemented
2C4×SD16×D59C211yesmaximal, characteristic
3D4×#11745659C211yesmaximal, characteristic
4#21422988C211yesmaximal, characteristic, complemented
5#21422985C211yesmaximal, characteristic, complemented
6#21422939C211yesmaximal, characteristic, complemented
7#21422936C211yesmaximal, characteristic, complemented
8#21422932C211yesmaximal, characteristic, complemented
9#21422929C211yesmaximal, characteristic, complemented
10SD16×C59⋊C8C211yesmaximal, characteristic, complemented
11#21422850C211yesmaximal, characteristic, complemented
12#21422523C211yesmaximal, characteristic, complemented
13#21422519C211yesmaximal, characteristic
14C8×#11745659C211yesmaximal, characteristic, complemented
15C8×SD16×C59C211yesmaximal, characteristic, complemented
16C2×SD16×D59C411yescharacteristic
17C22×#11745659—21no—
18C4×Q8×D59C2211yescharacteristic
19C4×D4×D59C2211yescharacteristic
20#16837532—21no—
21#16837532C2211yescharacteristic, complemented
22#16837529—21no—
23#16837529C2211yescharacteristic, complemented
24Q8×C59⋊C8C2211yescharacteristic, complemented
25#16837493C411yescharacteristic
26C4×#11745660C2211yescharacteristic
27SD16×Dic59C411yescharacteristic
28C4×#11745671C2211yescharacteristic
29#16837489C411yescharacteristic
30C4×#11745670C2211yescharacteristic
31#16837487C411yescharacteristic
32#16837481C2211yescharacteristic
33#16837479C2211yescharacteristic
34#16837473—21no—
35#16837470—21no—
36D4×C59⋊C8C2211yescharacteristic
37#16837453C2211yescharacteristic
38#106×D59C411yescharacteristic
39#16837424—21no—
40#16837424C2211yescharacteristic
41#16837424C2211yescharacteristic
42#103×D59C411yescharacteristic
43#102×D59C411yescharacteristic
44#16837364—21no—
45C4×#11745659—21no—
46C4×#11745659C2211yescharacteristic
47C4×C8×D59C2211yescharacteristic
48#16837153C2211yescharacteristic, complemented
49#16837152C2211yescharacteristic, complemented
50#16837152C2211yescharacteristic, complemented
51#16837134C2211yescharacteristic, complemented
52Q8⋊(C59⋊C8)C2211yescharacteristic, complemented
53#16837132C2211yescharacteristic, complemented
54#16837131C2211yescharacteristic
55D4⋊(C59⋊C8)C2211yescharacteristic
56#16837129C2211yescharacteristic
57#16837124C2211yescharacteristic, complemented
58#16837123C2211yescharacteristic, complemented
59C8×C59⋊C8C2211yescharacteristic, complemented
60C8×Q8×C59C2211yescharacteristic, complemented
61C4×SD16×C59C2211yescharacteristic
62C8×D4×C59C2211yescharacteristic
63C59×#334C2211yescharacteristic, complemented
64C59×Q8⋊C8C2211yescharacteristic, complemented
65C59×D4⋊C8C2211yescharacteristic
66C82×C59C2211yescharacteristic, complemented
67C2×Q8×D59C2×C411yescharacteristic
68C2×D4×D59C2×C411yescharacteristic
69C22×C4×D59—21no—
70C2×#11745660C2×C411yescharacteristic
71C2×#11745670C2×C411yescharacteristic
72C2×#11745671C2×C411yescharacteristic
73SD16×D59—24no—
74C2×#11745659—21no—
75C2×#11745659—21no—
76C2×#11745659—21no—
77C2×#11745659—21no—
78C2×#11745659—44no—
79C2×#11745659D411yescharacteristic
80C2×#11745659D411yescharacteristic
81C22×C59⋊C8—21no—
82C2×C8×D59C2×C411yescharacteristic
83C2×C8×D59C2×C411yescharacteristic
84Q8×Dic59C2×C411yescharacteristic
85C4×Dic118—21no—
86C4×Dic118C2311yescharacteristic
87#14273692—21no—
88#14273692C2×C411yescharacteristic
89C4×D236C2311yescharacteristic
90D4×Dic59C2×C411yescharacteristic
91#14273689C2×C411yescharacteristic
92C4×C22⋊D59—21no—
93(C22⋊D59)⋊C4—21no—
94C4⋊C4×D59—21no—
95C4⋊C4×D59C2×C411yescharacteristic
96C4⋊C4×D59C2×C411yescharacteristic
97C22⋊C4×D59—21no—
98C42×D59—21no—
99C42×D59C2311yescharacteristic
100#14273659C2×C411yescharacteristic
101#14273658C2×C411yescharacteristic
102#14273658C2×C411yescharacteristic
103C4⋊(C59⋊C8)—21no—
104C4⋊(C59⋊C8)C2311yescharacteristic
105C4⋊(C59⋊C8)C2311yescharacteristic
106Dic59⋊C8—21no—
107Dic59⋊C8—21no—
108Dic59⋊C8—21no—
109Dic59⋊C8—21no—
110Dic59⋊C8—21no—
111#14273652C2×C411yescharacteristic
112#14273651C2×C411yescharacteristic
113#14273650C2×C411yescharacteristic
114#14273649C2×C411yescharacteristic
115#14273648C2×C411yescharacteristic
116#14273647C2×C411yescharacteristic
117C22⋊(C59⋊C8)—21no—
118(C2×D59)⋊C8—21no—
119(C2×D59)⋊C8—21no—
120(C2×D59)⋊C8—21no—
121#14273637—21no—
122#14273637—21no—
123#14273637D411yescharacteristic
124#14273637D411yescharacteristic
125C4×C59⋊C8—21no—
126C4×C59⋊C8C2311yescharacteristic
127C4×C59⋊C8C2311yescharacteristic
128C4×C59⋊C8C2311yescharacteristic
129C8×Dic59C2×C411yescharacteristic
130C8×Dic59C2×C411yescharacteristic
131C2×SD16×C59C2×C411yescharacteristic
132C22×C8×C59—21no—
133C4×Q8×C59C2311yescharacteristic
134C4×D4×C59C2311yescharacteristic
135#106×C59C2×C411yescharacteristic
136C4⋊C8×C59—21no—
137C4⋊C8×C59C2311yescharacteristic
138C4⋊C8×C59C2311yescharacteristic
139#103×C59C2×C411yescharacteristic
140#102×C59C2×C411yescharacteristic
141C22⋊C8×C59—21no—
142C4×C8×C59—21no—
143C4×C8×C59C2311yescharacteristic
144C4×C8×C59C2311yescharacteristic
145C4×C8×C59C2311yescharacteristic
146C23×D59—21no—
147C2×Q8×C59C22×C411yescharacteristic
148C2×D4×C59C22×C411yescharacteristic
149C22×C4×C59—21no—
150C2×C22⋊D59—21no—
151C22×Dic59—21no—
152Q8×D59—22no—
153Q8×D59—41no—
154D4×D59—22no—
155D4×D59—41no—
156C2×D236C22×C411yescharacteristic
157C2×C4×D59—21no—
158C2×C4×D59—21no—
159C2×C4×D59—21no—
160C2×C4×D59—21no—
161C2×C4×D59—21no—
162C2×C4×D59—42no—
163C2×C4×D59—42no—
164C2×C4×D59C22×C411yescharacteristic
165C2×C4×D59C2×D411yescharacteristic
166C2×C4×D59#4111yescharacteristic
167C2×Dic118—21no—
168C2×Dic118C22×C411yescharacteristic
169SD16×C59M1614yescomplemented
170C2×C8×C59—21no—
171C2×C8×C59—21no—
172C2×C8×C59—21no—
173C2×C8×C59—42no—
174C2×C8×C59C22×C411yescharacteristic
175C2×C8×C59C22×C411yescharacteristic
176C2×C8×C59C2×D411yescharacteristic
177C2×C8×C59C2×D411yescharacteristic
178C4⋊C4×C59—21no—
179C4⋊C4×C59C22×C411yescharacteristic
180C4⋊C4×C59C22×C411yescharacteristic
181C22⋊C4×C59—21no—
182C42×C59—21no—
183C42×C59C2411yescharacteristic
184C22⋊Dic59—21no—
185#11745671—22no—
186#11745670—22no—
187(C2×D59)⋊C4—21no—
188(C2×D59)⋊C4—21no—
189C4⋊Dic59—21no—
190C4⋊Dic59C22×C411yescharacteristic
191C4⋊Dic59C22×C411yescharacteristic
192Dic59⋊C4—21no—
193Dic59⋊C4—21no—
194Dic59⋊C4—21no—
195Dic59⋊C4—21no—
196C4×Dic59—21no—
197C4×Dic59—21no—
198C4×Dic59—21no—
199C4×Dic59C22×C411yescharacteristic
200C4×Dic59C2×D411yescharacteristic
201C4×Dic59#4111yescharacteristic
202C2×C59⋊C8—21no—
203C2×C59⋊C8—21no—
204C2×C59⋊C8—21no—
205C2×C59⋊C8—42no—
206C2×C59⋊C8C22×C411yescharacteristic
207C2×C59⋊C8C22×C411yescharacteristic
208C2×C59⋊C8C2×D411yescharacteristic
209C2×C59⋊C8C2×D411yescharacteristic
210#11745660—22no—
211#11745659—22no—
212#11745659—42no—
213#11745659—42no—
214#11745659—42no—
215#11745659—42no—
216#11745659SD1614yesdirect product factor
217C8×D59—22no—
218C8×D59—41no—
219C23×C59—21no—
220C22×D59—21no—
221C22×D59—42no—
222C22×D59—42no—
223C22×D59—81no—
224C22×D59C4×D411yescharacteristic
225Q8×C59—21no—
226Q8×C59C2×M1612yescomplemented
227D4×C59—21no—
228D4×C59C2×M1612yes—
229C2×C4×C59—21no—
230C2×C4×C59—21no—
231C2×C4×C59—21no—
232C2×C4×C59—41no—
233C2×C4×C59—41no—
234C2×C4×C59C23×C411yescharacteristic
235C2×C4×C59C22×D411yescharacteristic
236C2×C4×C59C2×#4111yescharacteristic
237C22⋊D59—42no—
238C2×Dic59—21no—
239C2×Dic59—21no—
240C2×Dic59—21no—
241C2×Dic59—42no—
242C2×Dic59C4×D411yescharacteristic
243C2×Dic59C4×D411yescharacteristic
244C2×Dic59C4×D411yescharacteristic
245D236—21no—
246D236—21no—
247C4×D59—21no—
248C4×D59—21no—
249C4×D59—41no—
250C4×D59—42no—
251C4×D59—42no—
252C4×D59—41no—
253C4×D59—41no—
254C4×D59—42no—
255C4×D59—81no—
256C4×D59C2×SD1612yes—
257C4×D59#13512yes—
258Dic118—21no—
259Dic118—21no—
260Dic118—42no—
261C8×C59—21no—
262C8×C59—21no—
263C8×C59—41no—
264C8×C59—41no—
265C8×C59—41no—
266C8×C59C2×M1612yescomplemented
267C8×C59C2×SD1612yescomplemented
268C59⋊C8—21no—
269C59⋊C8—21no—
270C59⋊C8—21no—
271C59⋊C8—41no—
272C59⋊C8—41no—
273C59⋊C8—41no—
274C59⋊C8C2×SD1612yescomplemented
275M16×SD16—591nomaximal, Sylow
276C22×C59—22no—
277C22×C59—41no—
278C22×C59—41no—
279C22×C59C2×C4×D411yescharacteristic
280C2×D59—21no—
281C2×D59—21no—
282C2×D59—41no—
283C2×D59—41no—
284C2×D59—41no—
285C2×D59—84no—
286C2×D59C4×SD1612yes—
287C4×C59—22no—
288C4×C59—21no—
289C4×C59—41no—
290C4×C59—41no—
291C4×C59C22×M1611yescharacteristic
292C4×C59#56811yescharacteristic
293C4×C59C22×SD1611yescharacteristic
294C4×C59C2×#13511yescharacteristic
295Dic59—21no—
296Dic59—21no—
297Dic59—41no—
298Dic59—41no—
299Dic59—41no—
300Dic59C4×SD1612yes—
301Q8×M16—591no—
302C2×C4×SD16—591no—
303D4×M16—591no—
304#1590—591no—
305#1590—591no—
306#1583—591no—
307#1583—591no—
308#1582—591no—
309#1582—591no—
310C8×SD16—591no—
311C8×SD16D5911yescharacteristic, complemented
312#1566—591no—
313#1487—591no—
314#1486—591no—
315C8×M16—591no—
316C2×C59—42no—
317C2×C59D4×M1611yescharacteristic
318C2×C59C2×C4×SD1611yescharacteristic
319C2×C59#295711yescharacteristic
320D59—22no—
321D59—81no—
322C22×SD16—591no—
323C22×M16—1181no—
324C2×C4×Q8—591no—
325C2×C4×D4—591no—
326#446—591no—
327#446—591no—
328#446—1181no—
329#446—1181no—
330C8×Q8—591no—
331C8×Q8C2×D5911yescharacteristic, complemented
332C4×SD16—591no—
333C4×SD16—591no—
334C4×SD16—591no—
335C4×SD16—591no—
336C4×SD16—591no—
337C4×SD16—591no—
338C4×SD16—591no—
339C4×SD16C2×D5911yescharacteristic
340#436—591no—
341#436—591no—
342#435—1181no—
343#435—1181no—
344C8×D4—591no—
345C8×D4C2×D5911yescharacteristic
346#431—591no—
347C2×#106—591no—
348#423—591no—
349#423—591no—
350#423—1181no—
351C2×#103—591no—
352C2×#102—591no—
353#407—1181no—
354C4×M16—591no—
355C4×M16—1181no—
356C2×C4×C8—591no—
357#334—591no—
358#334—591no—
359#334—591no—
360#334C2×D5911yescharacteristic, complemented
361Q8⋊C8—591no—
362Q8⋊C8—591no—
363Q8⋊C8—591no—
364Q8⋊C8C2×D5911yescharacteristic, complemented
365D4⋊C8—591no—
366D4⋊C8—591no—
367D4⋊C8—591no—
368D4⋊C8C2×D5911yescharacteristic
369#322—591no—
370#322—591no—
371C82—591no—
372C82C2×D5911yescharacteristic, complemented
373C59M16×SD1611yescharacteristic, complemented, Sylow
374C22×Q8—591no—
375C22×D4—591no—
376C23×C4—1181no—
377C2×SD16—591no—
378C2×SD16—591no—
379C2×SD16—591no—
380C2×SD16—1184no—
381C2×SD16C4×D5911yescharacteristic
382C2×M16—591no—
383C2×M16—591no—
384C2×M16—1181no—
385C2×M16—1181no—
386C2×M16—1181no—
387C2×M16—1181no—
388C2×M16—2364no—
389C22×C8—21no—
390C22×C8—591no—
391C22×C8—591no—
392C22×C8—1181no—
393C4×Q8—591no—
394C4×Q8—591no—
395C4×Q8—591no—
396C4×Q8—1181no—
397C4×Q8—1181no—
398C4×Q8C22×D5911yescharacteristic
399C4×D4—591no—
400C4×D4—591no—
401C4×D4—591no—
402C4×D4—1181no—
403C4×D4—1181no—
404C4×D4C22×D5911yescharacteristic
405C2×C4⋊C4—591no—
406C2×C4⋊C4—591no—
407C2×C4⋊C4—1181no—
408C2×C22⋊C4—1181no—
409C2×C42—591no—
410C2×C42—1181no—
411#106—591no—
412#106—591no—
413#106—591no—
414#106C4×D5911yescharacteristic
415C4⋊C8—21no—
416C4⋊C8—591no—
417C4⋊C8—591no—
418C4⋊C8—1181no—
419C4⋊C8—1181no—
420C4⋊C8—1181no—
421C4⋊C8—1181no—
422C4⋊C8—1181no—
423C4⋊C8—1181no—
424C4⋊C8C22×D5911yescharacteristic
425C4⋊C8C22×D5911yescharacteristic
426#103—591no—
427#103—591no—
428#103—591no—
429#103C4×D5911yescharacteristic
430#102—591no—
431#102—591no—
432#102—591no—
433#102C4×D5911yescharacteristic
434C22⋊C8—21no—
435C22⋊C8—1181no—
436C22⋊C8—1181no—
437C22⋊C8—1181no—
438C22⋊C8—1181no—
439#97—591no—
440#97—591no—
441#97—1181no—
442#97—1181no—
443C4×C8—21no—
444C4×C8—591no—
445C4×C8—591no—
446C4×C8—591no—
447C4×C8—591no—
448C4×C8—591no—
449C4×C8—1181no—
450C4×C8C22×D5911yescharacteristic
451C4×C8C22×D5911yescharacteristic
452C4×C8C22×D5911yescharacteristic
453C24—1181no—
454C2×Q8—591no—
455C2×Q8—1181no—
456C2×Q8—1182no—
457C2×Q8—2361no—
458C2×Q8C2×C4×D5911yescharacteristic
459C2×D4—591no—
460C2×D4—1181no—
461C2×D4—1182no—
462C2×D4—2361no—
463C2×D4C2×C4×D5911yescharacteristic
464C22×C4—21no—
465C22×C4—591no—
466C22×C4—591no—
467C22×C4—591no—
468C22×C4—1181no—
469C22×C4—1181no—
470C22×C4—1181no—
471C22×C4—1181no—
472C22×C4—1181no—
473C22×C4—1181no—
474C22×C4—2362no—
475C22×C4—2362no—
476SD16—1182no—
477SD16—1182no—
478SD16—1182no—
479SD16#1174565914yesdirect product factor
480M16—594no—
481M16—1182no—
482M16—2362no—
483M16—2362no—
484M16—2362no—
485M16—2362no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—42no—
490C2×C8—591no—
491C2×C8—591no—
492C2×C8—591no—
493C2×C8—591no—
494C2×C8—1182no—
495C2×C8—1181no—
496C2×C8—1181no—
497C2×C8—1181no—
498C2×C8—2361no—
499C2×C8—2362no—
500C2×C8C2×C4×D5911yescharacteristic
501C2×C8C2×C4×D5911yescharacteristic
502C2×C8D4×D5911yescharacteristic
503C2×C8D4×D5911yescharacteristic
504C4⋊C4—21no—
505C4⋊C4—591no—
506C4⋊C4—591no—
507C4⋊C4—1181no—
508C4⋊C4—1181no—
509C4⋊C4—1181no—
510C4⋊C4—1181no—
511C4⋊C4—1181no—
512C4⋊C4C2×C4×D5911yescharacteristic
513C4⋊C4C2×C4×D5911yescharacteristic
514C22⋊C4—21no—
515C22⋊C4—1181no—
516C22⋊C4—1181no—
517C22⋊C4—1181no—
518C42—21no—
519C42—591no—
520C42—591no—
521C42—591no—
522C42—1181no—
523C42—1181no—
524C42—1181no—
525C42C23×D5911yescharacteristic
526C23—21no—
527C23—591no—
528C23—1181no—
529C23—4721no—
530C23—2362no—
531C23—2362no—
532Q8—21no—
533Q8—1181no—
534Q8—1181no—
535Q8—2362no—
536Q8C2×#1174565912yescomplemented
537D4—21no—
538D4—1181no—
539D4—1181no—
540D4—2362no—
541D4C2×#1174565912yes—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—591no—
548C2×C4—592no—
549C2×C4—592no—
550C2×C4—591no—
551C2×C4—591no—
552C2×C4—1181no—
553C2×C4—1181no—
554C2×C4—1181no—
555C2×C4—1181no—
556C2×C4—1181no—
557C2×C4—4721no—
558C2×C4—2361no—
559C2×C4—2362no—
560C2×C4—2362no—
561C2×C4—2362no—
562C2×C4—2362no—
563C2×C4—2361no—
564C2×C4—2361no—
565C2×C4C22×C4×D5911yescharacteristic
566C2×C4C2×D4×D5911yescharacteristic
567C2×C4#41×D5911yescharacteristic
568C8—21no—
569C8—21no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—592no—
574C8—1181no—
575C8—1181no—
576C8—1181no—
577C8—2361no—
578C8—2361no—
579C8—2361no—
580C8C2×#1174565912yescomplemented
581C8SD16×D5912yescomplemented
582C22—22no—
583C22—41no—
584C22—41no—
585C22—592no—
586C22—1181no—
587C22—1181no—
588C22—4724no—
589C22—2361no—
590C22—2361no—
591C22—2361no—
592C22C4×D4×D5911yescharacteristic
593C4—21no—
594C4—22no—
595C4—41no—
596C4—41no—
597C4—592no—
598C4—1181no—
599C4—1181no—
600C4—2361no—
601C4—2361no—
602C4—2361no—
603C4C22×#1174565911yescharacteristic
604C4#1683816711yescharacteristic
605C4C2×SD16×D5911yescharacteristic
606C4#135×D5911yescharacteristic
607C2—42no—
608C2—1182no—
609C2—4721no—
610C2D4×#1174565911yescharacteristic
611C2C4×SD16×D5911yescharacteristic
612C2#2143300811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC8×SD16×C59C2
socleC22×C59C2×C4×D4
prime radicalC2×D4×D59C2×C4
cosocleC42×C59C24
hypercenterC8×SD16D59
hypocenterC59M16×SD16
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
1. Q8×#11745659C2semidirect
4. #21422988C2semidirect
5. #21422985C2semidirect
6. #21422939C2semidirect
7. #21422936C2semidirect
8. #21422932C2semidirect
9. #21422929C2semidirect
10. SD16×C59⋊C8C2semidirect
11. #21422850C2semidirect
12. #21422523C2semidirect
14. C8×#11745659C2semidirect
15. C8×SD16×C59C2semidirect
21. #16837532C22semidirect
23. #16837529C22semidirect
24. Q8×C59⋊C8C22semidirect
48. #16837153C22semidirect
49. #16837152C22semidirect
50. #16837152C22semidirect
51. #16837134C22semidirect
52. Q8⋊(C59⋊C8)C22semidirect
53. #16837132C22semidirect
57. #16837124C22semidirect
58. #16837123C22semidirect
59. C8×C59⋊C8C22semidirect
60. C8×Q8×C59C22semidirect
63. C59×#334C22semidirect
64. C59×Q8⋊C8C22semidirect
66. C82×C59C22semidirect
169. SD16×C59M16semidirect
216. #11745659SD16direct (N × H)
226. Q8×C59C2×M16semidirect
266. C8×C59C2×M16semidirect
267. C8×C59C2×SD16semidirect
274. C59⋊C8C2×SD16semidirect
311. C8×SD16D59semidirect
331. C8×Q8C2×D59semidirect
360. #334C2×D59semidirect
364. Q8⋊C8C2×D59semidirect
372. C82C2×D59semidirect
373. C59M16×SD16semidirect
479. SD16#11745659direct (N × H)
536. Q8C2×#11745659semidirect
580. C8C2×#11745659semidirect
581. C8SD16×D59semidirect

Maximal subgroups

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

subgroupindex
Q8×#117456592
C4×SD16×D592
D4×#117456592
#214229882
#214229852
#214229392
#214229362
#214229322
#214229292
SD16×C59⋊C82
#214228502
#214225232
#214225192
C8×#117456592
C8×SD16×C592
M16×SD1659