Finite Group Databasebeta

← D59×#2088 #28617731

Subgroups — D59×#2088 #28617731

Order 15104.

1054 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#106×D59C211yesmaximal, characteristic
2C2×C4⋊C8×D59C211yesmaximal, characteristic
3#389×D59C211yesmaximal, characteristic
4#389×D59C211yesmaximal, characteristic
5#21425600C211yesmaximal, characteristic, complemented
6#21425599C211yesmaximal, characteristic, complemented
7#21425598C211yesmaximal, characteristic, complemented
8#21425597C211yesmaximal, characteristic, complemented
9#21425596C211yesmaximal, characteristic, complemented
10#21425595C211yesmaximal, characteristic, complemented
11#21425594C211yesmaximal, characteristic, complemented
12#340×D59C211yesmaximal, characteristic
13#340×D59C211yesmaximal, characteristic
14#340×D59C211yesmaximal, characteristic
15C59×#2088C211yesmaximal, characteristic, complemented
16C22×C8×D59C2211yescharacteristic
17C22×C8×D59C2211yescharacteristic
18C2×C4⋊C4×D59—21no—
19C2×C4⋊C4×D59—21no—
20C2×C4⋊C4×D59C2211yescharacteristic
21C2×C4⋊C4×D59C2211yescharacteristic
22C2×C4⋊C4×D59C2211yescharacteristic
23C2×C4⋊C4×D59C2211yescharacteristic
24C2×C42×D59C2211yescharacteristic
25C2×#14273659C2211yescharacteristic
26C2×#14273658C2211yescharacteristic
27C2×#14273658C2211yescharacteristic
28#106×D59—24no—
29C2×C4⋊(C59⋊C8)C2211yescharacteristic
30C2×Dic59⋊C8C2211yescharacteristic
31C2×Dic59⋊C8C2211yescharacteristic
32C4⋊C8×D59—24no—
33#16837301C2211yescharacteristic
34#16837301C2211yescharacteristic
35#16837300C2211yescharacteristic
36#16837300C2211yescharacteristic
37#16837299—21no—
38#16837299—21no—
39#16837298C2211yescharacteristic
40#16837298C2211yescharacteristic
41#16837297—21no—
42#16837297—21no—
43#95×D59—21no—
44#95×D59—21no—
45#16837165C2211yescharacteristic
46#16837165C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837164C2211yescharacteristic
52#16837164C2211yescharacteristic
53#16837164C2211yescharacteristic
54C2×#106×C59C2211yescharacteristic
55C2×C4⋊C8×C59C2211yescharacteristic
56C59×#389C2211yescharacteristic
57C59×#389C2211yescharacteristic
58C59×#340C2211yescharacteristic
59C59×#340C2211yescharacteristic
60C59×#340C2211yescharacteristic
61C22×C4×D59—21no—
62C22×C4×D59—21no—
63C22×C4×D59—21no—
64C22×C4×D59—21no—
65C22×C4×D59D411yescharacteristic
66C22×C4×D59D411yescharacteristic
67C22×C4×D59C2311yescharacteristic
68C22×C59⋊C8C2311yescharacteristic
69C22×C59⋊C8C2311yescharacteristic
70C2×C8×D59—22no—
71C2×C8×D59—22no—
72C2×C8×D59—22no—
73C2×C8×D59—22no—
74C2×C8×D59—22no—
75C2×C8×D59D414yes—
76C2×C4⋊Dic59—21no—
77C2×C4⋊Dic59—21no—
78C2×C4⋊Dic59C2311yescharacteristic
79C2×C4⋊Dic59C2311yescharacteristic
80C2×C4⋊Dic59C2311yescharacteristic
81C2×C4⋊Dic59C2311yescharacteristic
82C2×Dic59⋊C4—21no—
83C2×Dic59⋊C4—21no—
84C2×Dic59⋊C4—21no—
85C2×Dic59⋊C4—21no—
86C2×Dic59⋊C4—21no—
87C2×Dic59⋊C4—21no—
88C2×Dic59⋊C4—21no—
89C2×Dic59⋊C4—21no—
90C4⋊C4×D59—22no—
91C4⋊C4×D59—22no—
92C4⋊C4×D59—22no—
93C4⋊C4×D59—22no—
94C4⋊C4×D59—22no—
95C4⋊C4×D59—22no—
96C4⋊C4×D59—44no—
97C4⋊C4×D59—44no—
98C4⋊C4×D59Q814yes—
99C4⋊C4×D59Q814yes—
100C2×C4×Dic59D411yescharacteristic
101C2×C4×Dic59D411yescharacteristic
102C2×C4×Dic59C2311yescharacteristic
103C42×D59—22no—
104C42×D59—22no—
105#14273659—22no—
106#14273658—22no—
107#14273658—22no—
108C4⋊(C59⋊C8)—22no—
109Dic59⋊C8—22no—
110Dic59⋊C8—22no—
111C59⋊#95—21no—
112C59⋊#95—21no—
113C59⋊#95—21no—
114C59⋊#95—21no—
115C59⋊#95—21no—
116C59⋊#95—21no—
117C22×C8×C59C2311yescharacteristic
118C22×C8×C59C2311yescharacteristic
119C2×C4⋊C4×C59—21no—
120C2×C4⋊C4×C59—21no—
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C4⋊C4×C59C2311yescharacteristic
124C2×C4⋊C4×C59C2311yescharacteristic
125C2×C42×C59C2311yescharacteristic
126#106×C59—22no—
127C4⋊C8×C59—22no—
128#95×C59—21no—
129#95×C59—21no—
130C23×D59C2×D411yescharacteristic
131C22×C4×C59—21no—
132C22×C4×C59—21no—
133C22×C4×C59—21no—
134C22×C4×C59—21no—
135C22×C4×C59C2×D411yescharacteristic
136C22×C4×C59C2×D411yescharacteristic
137C22×C4×C59C2411yescharacteristic
138C22×Dic59—21no—
139C22×Dic59—21no—
140C22×Dic59—21no—
141C22×Dic59—21no—
142C22×Dic59C2×D411yescharacteristic
143C22×Dic59C2×D411yescharacteristic
144C22×Dic59C2×D411yescharacteristic
145C2×C4×D59—22no—
146C2×C4×D59—22no—
147C2×C4×D59—22no—
148C2×C4×D59—24no—
149C2×C4×D59—24no—
150C2×C4×D59—22no—
151C2×C4×D59—22no—
152C2×C4×D59—42no—
153C2×C4×D59—42no—
154C2×C4×D59—42no—
155C2×C4×D59—42no—
156C2×C4×D59—42no—
157C2×C4×D59—42no—
158C2×C4×D59—42no—
159C2×C4×D59—42no—
160C2×C4×D59—42no—
161C2×C4×D59—42no—
162C2×C4×D59SD1614yes—
163C2×C4×D59C2×D412yes—
164C2×C4×D59C2×Q812yes—
165C2×C4×D59C2×Q812yes—
166C2×C4×D59#4112yes—
167C2×C4×D59#4112yes—
168C2×C4×D59#4112yes—
169C2×C8×C59—21no—
170C2×C8×C59—21no—
171C2×C8×C59—21no—
172C2×C8×C59—21no—
173C2×C8×C59—21no—
174C2×C8×C59C2×D412yes—
175C4⋊C4×C59—21no—
176C4⋊C4×C59—21no—
177C4⋊C4×C59—21no—
178C4⋊C4×C59—21no—
179C4⋊C4×C59—21no—
180C4⋊C4×C59—21no—
181C4⋊C4×C59—42no—
182C4⋊C4×C59—42no—
183C4⋊C4×C59C2×Q812yes—
184C4⋊C4×C59C2×Q812yes—
185C42×C59—21no—
186C42×C59—21no—
187C4⋊Dic59—21no—
188C4⋊Dic59—21no—
189C4⋊Dic59—21no—
190C4⋊Dic59—21no—
191C4⋊Dic59—21no—
192C4⋊Dic59—21no—
193C4⋊Dic59—42no—
194C4⋊Dic59—42no—
195C4⋊Dic59C2×Q812yes—
196C4⋊Dic59C2×Q812yes—
197Dic59⋊C4—24no—
198Dic59⋊C4—24no—
199Dic59⋊C4—42no—
200Dic59⋊C4—42no—
201Dic59⋊C4—42no—
202Dic59⋊C4—42no—
203Dic59⋊C4—42no—
204Dic59⋊C4—42no—
205C4×Dic59—21no—
206C4×Dic59—21no—
207C4×Dic59—22no—
208C4×Dic59—22no—
209C2×C59⋊C8—21no—
210C2×C59⋊C8—21no—
211C2×C59⋊C8—21no—
212C2×C59⋊C8—21no—
213C2×C59⋊C8—21no—
214C2×C59⋊C8C2×D412yes—
215C8×D59—28no—
216C8×D59—44no—
217C23×C59C22×D411yescharacteristic
218C22×D59#12112yes—
219C22×D59C22⋊Q812yes—
220C22×D59C22⋊Q812yes—
221C22×D59C2×SD1612yes—
222C22×D59#13512yes—
223C22×D59AGL(1,ℤ/8)12yes—
224C22×D59#13712yes—
225C2×C4×C59—21no—
226C2×C4×C59—21no—
227C2×C4×C59—21no—
228C2×C4×C59—22no—
229C2×C4×C59—22no—
230C2×C4×C59—21no—
231C2×C4×C59—21no—
232C2×C4×C59—41no—
233C2×C4×C59—41no—
234C2×C4×C59—41no—
235C2×C4×C59—41no—
236C2×C4×C59—41no—
237C2×C4×C59—41no—
238C2×C4×C59—41no—
239C2×C4×C59—41no—
240C2×C4×C59—41no—
241C2×C4×C59—41no—
242C2×C4×C59C2×SD1612yes—
243C2×C4×C59C22×D411yescharacteristic
244C2×C4×C59C22×Q811yescharacteristic
245C2×C4×C59C22×Q811yescharacteristic
246C2×C4×C59C2×#4111yescharacteristic
247C2×C4×C59C2×#4111yescharacteristic
248C2×C4×C59C2×#4111yescharacteristic
249C2×Dic59—21no—
250C2×Dic59—21no—
251C2×Dic59—21no—
252C2×Dic59—22no—
253C2×Dic59—22no—
254C2×Dic59—21no—
255C2×Dic59—21no—
256C2×Dic59—41no—
257C2×Dic59—41no—
258C2×Dic59—41no—
259C2×Dic59—41no—
260C2×Dic59—41no—
261C2×Dic59—41no—
262C2×Dic59—41no—
263C2×Dic59—41no—
264C2×Dic59—41no—
265C2×Dic59—41no—
266C2×Dic59#12112yes—
267C2×Dic59C22⋊Q812yes—
268C2×Dic59C22⋊Q812yes—
269C2×Dic59C2×SD1612yes—
270C4×D59—28no—
271C4×D59—44no—
272C4×D59—48no—
273C4×D59—48no—
274C4×D59—84no—
275C4×D59—84no—
276C4×D59#12314yes—
277C4×D59#12514yes—
278C4×D59#12514yes—
279C4×D59C4⋊Q814yes—
280C8×C59—22no—
281C8×C59—41no—
282C59⋊C8—22no—
283C59⋊C8—41no—
284C2×#2088—591nomaximal, Sylow
285C22×C59C2×#12111yescharacteristic
286C22×C59C2×C22⋊Q811yescharacteristic
287C22×C59C2×C22⋊Q811yescharacteristic
288C22×C59C22×SD1611yescharacteristic
289C22×C59C2×#13511yescharacteristic
290C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
291C22×C59C2×#13711yescharacteristic
292C2×D59#39814yes—
293C2×D59#46514yes—
294C2×D59#46814yes—
295C2×D59#47514yes—
296C2×D59#47614yes—
297C2×D59#47814yes—
298C2×D59#47914yes—
299C4×C59—22no—
300C4×C59—42no—
301C4×C59—41no—
302C4×C59—42no—
303C4×C59—81no—
304C4×C59—81no—
305C4×C59C2×#12311yescharacteristic
306C4×C59C2×#12511yescharacteristic
307C4×C59C2×#12511yescharacteristic
308C4×C59C2×C4⋊Q811yescharacteristic
309Dic59—22no—
310Dic59—42no—
311Dic59—41no—
312Dic59—42no—
313Dic59—81no—
314Dic59—81no—
315Dic59#39814yes—
316C22×#106—591no—
317C22×C4⋊C8—591no—
318C2×#389—591no—
319C2×#389—591no—
320#2088—591no—
321#2088—591no—
322#2088—591no—
323#2088—591no—
324#2088—591no—
325#2088—591no—
326#2088—591no—
327#2088D5911yescharacteristic, direct product factor
328C2×#340—591no—
329C2×#340—591no—
330C2×#340—591no—
331C2×C59C2×#39811yescharacteristic
332C2×C59C2×#46511yescharacteristic
333C2×C59C2×#46811yescharacteristic
334C2×C59C2×#47611yescharacteristic
335C2×C59C2×#47811yescharacteristic
336C2×C59C2×#47511yescharacteristic
337C2×C59C2×#47911yescharacteristic
338D59#208818yesdirect product factor
339C23×C8—591no—
340C23×C8—591no—
341C22×C4⋊C4—591no—
342C22×C4⋊C4—591no—
343C22×C4⋊C4—591no—
344C22×C4⋊C4—591no—
345C22×C4⋊C4—1181no—
346C22×C4⋊C4—1181no—
347C22×C42—591no—
348C2×#106—591no—
349C2×#106—591no—
350C2×#106—591no—
351C2×#106—1184no—
352C2×#106C2×D5911yescharacteristic
353C2×C4⋊C8—591no—
354C2×C4⋊C8—591no—
355C2×C4⋊C8—591no—
356C2×C4⋊C8—1184no—
357C2×C4⋊C8C2×D5911yescharacteristic
358#389—591no—
359#389—591no—
360#389—591no—
361#389—591no—
362#389—591no—
363#389—591no—
364#389—1181no—
365#389—1181no—
366#389—1181no—
367#389—1181no—
368#389C2×D5911yescharacteristic
369#389C2×D5911yescharacteristic
370C2×#95—1181no—
371C2×#95—1181no—
372#340—591no—
373#340—591no—
374#340—591no—
375#340—591no—
376#340—591no—
377#340—591no—
378#340—591no—
379#340—591no—
380#340—591no—
381#340C2×D5911yescharacteristic
382#340C2×D5911yescharacteristic
383#340C2×D5911yescharacteristic
384C59C2×#208811yescharacteristic, complemented, Sylow
385C23×C4—591no—
386C23×C4—591no—
387C23×C4—591no—
388C23×C4—1181no—
389C23×C4—1181no—
390C23×C4—1181no—
391C23×C4—1181no—
392C22×C8—591no—
393C22×C8—594no—
394C22×C8—591no—
395C22×C8—1182no—
396C22×C8—1182no—
397C22×C8—1182no—
398C22×C8—1182no—
399C22×C8—1182no—
400C22×C8C22×D5911yescharacteristic
401C22×C8C22×D5911yescharacteristic
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—591no—
405C2×C4⋊C4—591no—
406C2×C4⋊C4—594no—
407C2×C4⋊C4—594no—
408C2×C4⋊C4—591no—
409C2×C4⋊C4—591no—
410C2×C4⋊C4—1182no—
411C2×C4⋊C4—1182no—
412C2×C4⋊C4—1182no—
413C2×C4⋊C4—1182no—
414C2×C4⋊C4—1182no—
415C2×C4⋊C4—1182no—
416C2×C4⋊C4—1181no—
417C2×C4⋊C4—1181no—
418C2×C4⋊C4—1181no—
419C2×C4⋊C4—1181no—
420C2×C4⋊C4—1181no—
421C2×C4⋊C4—1181no—
422C2×C4⋊C4—1181no—
423C2×C4⋊C4—1181no—
424C2×C4⋊C4—1181no—
425C2×C4⋊C4—1181no—
426C2×C4⋊C4—2364no—
427C2×C4⋊C4—2364no—
428C2×C4⋊C4C22×D5911yescharacteristic
429C2×C4⋊C4C22×D5911yescharacteristic
430C2×C4⋊C4C22×D5911yescharacteristic
431C2×C4⋊C4C22×D5911yescharacteristic
432C2×C42—591no—
433C2×C42—591no—
434C2×C42—591no—
435C2×C42—1182no—
436C2×C42—1182no—
437C2×C42C22×D5911yescharacteristic
438#106—22no—
439#106—1182no—
440#106—1182no—
441#106—1182no—
442C4⋊C8—22no—
443C4⋊C8—1182no—
444C4⋊C8—1182no—
445C4⋊C8—1182no—
446#95—21no—
447#95—21no—
448#95—1181no—
449#95—1181no—
450#95—1181no—
451#95—1181no—
452#95—1181no—
453#95—1181no—
454C24—591no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—591no—
460C22×C4—592no—
461C22×C4—592no—
462C22×C4—592no—
463C22×C4—592no—
464C22×C4—592no—
465C22×C4—592no—
466C22×C4—591no—
467C22×C4—594no—
468C22×C4—591no—
469C22×C4—1182no—
470C22×C4—1182no—
471C22×C4—1182no—
472C22×C4—1184no—
473C22×C4—1184no—
474C22×C4—1182no—
475C22×C4—1182no—
476C22×C4—1181no—
477C22×C4—1181no—
478C22×C4—1181no—
479C22×C4—1181no—
480C22×C4—2362no—
481C22×C4—2362no—
482C22×C4—2362no—
483C22×C4—2362no—
484C22×C4—2362no—
485C22×C4—2362no—
486C22×C4—2362no—
487C22×C4—2362no—
488C22×C4—2362no—
489C22×C4—2362no—
490C22×C4D4×D5911yescharacteristic
491C22×C4D4×D5911yescharacteristic
492C22×C4C23×D5911yescharacteristic
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—592no—
499C2×C8—1188no—
500C2×C8—1181no—
501C2×C8—1181no—
502C2×C8—1181no—
503C2×C8—1181no—
504C2×C8—1181no—
505C2×C8—2364no—
506C2×C8D4×D5912yes—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—42no—
514C4⋊C4—42no—
515C4⋊C4—592no—
516C4⋊C4—592no—
517C4⋊C4—1184no—
518C4⋊C4—1184no—
519C4⋊C4—1181no—
520C4⋊C4—1181no—
521C4⋊C4—1181no—
522C4⋊C4—1181no—
523C4⋊C4—1181no—
524C4⋊C4—1181no—
525C4⋊C4—2362no—
526C4⋊C4—2362no—
527C4⋊C4—2362no—
528C4⋊C4—2362no—
529C4⋊C4—2362no—
530C4⋊C4—2362no—
531C4⋊C4—2362no—
532C4⋊C4—2362no—
533C4⋊C4Q8×D5912yes—
534C4⋊C4Q8×D5912yes—
535C42—21no—
536C42—21no—
537C42—1182no—
538C42—1182no—
539C42—1181no—
540C42—1181no—
541C23—592no—
542C23—592no—
543C23—592no—
544C23—592no—
545C23—592no—
546C23—592no—
547C23—592no—
548C23C2×D4×D5911yescharacteristic
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—592no—
567C2×C4—592no—
568C2×C4—592no—
569C2×C4—594no—
570C2×C4—594no—
571C2×C4—594no—
572C2×C4—594no—
573C2×C4—592no—
574C2×C4—1188no—
575C2×C4—1181no—
576C2×C4—1181no—
577C2×C4—1181no—
578C2×C4—1182no—
579C2×C4—1182no—
580C2×C4—1181no—
581C2×C4—1181no—
582C2×C4—4724no—
583C2×C4—4724no—
584C2×C4—2364no—
585C2×C4—2368no—
586C2×C4—2368no—
587C2×C4—2361no—
588C2×C4—2361no—
589C2×C4—2361no—
590C2×C4—2361no—
591C2×C4—2361no—
592C2×C4—2361no—
593C2×C4—2361no—
594C2×C4—2361no—
595C2×C4—2361no—
596C2×C4—2361no—
597C2×C4SD16×D5912yes—
598C2×C4C2×D4×D5911yescharacteristic
599C2×C4C2×Q8×D5911yescharacteristic
600C2×C4C2×Q8×D5911yescharacteristic
601C2×C4#41×D5911yescharacteristic
602C2×C4#41×D5911yescharacteristic
603C2×C4#41×D5911yescharacteristic
604C8—22no—
605C8—41no—
606C8—1182no—
607C8—2361no—
608C22—594no—
609C22—594no—
610C22—594no—
611C22—594no—
612C22—594no—
613C22—594no—
614C22—594no—
615C22#121×D5911yescharacteristic
616C22C22⋊Q8×D5911yescharacteristic
617C22C22⋊Q8×D5911yescharacteristic
618C22C2×SD16×D5911yescharacteristic
619C22#135×D5911yescharacteristic
620C22AGL(1,ℤ/8)×D5911yescharacteristic
621C22#137×D5911yescharacteristic
622C4—22no—
623C4—41no—
624C4—42no—
625C4—42no—
626C4—81no—
627C4—81no—
628C4—594no—
629C4—1182no—
630C4—4721no—
631C4—4721no—
632C4—2361no—
633C4—2362no—
634C4—2362no—
635C4#123×D5911yescharacteristic
636C4#125×D5911yescharacteristic
637C4#125×D5911yescharacteristic
638C4C4⋊Q8×D5911yescharacteristic
639C2—598no—
640C2#398×D5911yescharacteristic
641C2#465×D5911yescharacteristic
642C2#468×D5911yescharacteristic
643C2#476×D5911yescharacteristic
644C2#478×D5911yescharacteristic
645C2#475×D5911yescharacteristic
646C2#479×D5911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2088C2
socleC23×C59C22×D4
prime radicalC23×D59C2×D4
hypercenter#2088D59
hypocenterC59C2×#2088
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2088

Complements

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

NH ≅ G/Ntype
5. #21425600C2semidirect
6. #21425599C2semidirect
7. #21425598C2semidirect
8. #21425597C2semidirect
9. #21425596C2semidirect
10. #21425595C2semidirect
11. #21425594C2semidirect
15. C59×#2088C2semidirect
327. #2088D59direct (N × H)
338. D59#2088direct (N × H)
384. C59C2×#2088semidirect

Maximal subgroups

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

subgroupindex
C2×#106×D592
C2×C4⋊C8×D592
#389×D592
#214256002
#214255992
#214255982
#214255972
#214255962
#214255952
#214255942
#340×D592
C59×#20882
C2×#208859