Finite Group Databasebeta

← #28514764

Subgroups — #28514764

Order 15104.

1822 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837337C211yesmaximal, characteristic
2C2×#16837283C212yesmaximal, complemented
3C2×#16837273C212yesmaximal
4C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic
5#21422364C211yesmaximal, characteristic, complemented
6#21422359C211yesmaximal, characteristic, complemented
7#21422338C211yesmaximal, characteristic
8#21422332C212yesmaximal
9Dic59⋊#95C212yesmaximal, complemented
10C4×C59⋊#95C211yesmaximal, characteristic, complemented
11C2×C59×#389C211yesmaximal, characteristic, complemented
12C23×C4×D59C2211yescharacteristic
13C22×Dic59⋊C4C2212yes—
14C22×Dic59⋊C4C2212yes—
15C22×(C2×D59)⋊C4C2212yes—
16C22×(C2×D59)⋊C4C2211yescharacteristic
17C22×(C2×D59)⋊C4C2212yes—
18C22×(C2×D59)⋊C4C2211yescharacteristic
19C22×C4×Dic59C2211yescharacteristic
20C22×C4×Dic59C2212yes—
21#16837337C418yescomplemented
22#16837283—28no—
23#16837273—28no—
24C4×(C2×D59)⋊C4—24no—
25C2×C59⋊#95C2211yescharacteristic
26C2×C59⋊#95C2212yes—
27C2×C59⋊#95C2211yescharacteristic
28C2×C59⋊#95C2212yes—
29C2×C59⋊#95C2212yes—
30C2×C59⋊#95C2212yes—
31C2×C59⋊#95C2211yescharacteristic
32C2×C59⋊#95C2211yescharacteristic
33C2×C59⋊#95C2212yes—
34C22×C4⋊C4×C59C2212yes—
35C22×C4⋊C4×C59C2211yescharacteristic
36C22×C4⋊C4×C59C2211yescharacteristic
37C22×C42×C59C2211yescharacteristic
38C59×#389—24no—
39C2×#95×C59C2212yes—
40C24×D59C2311yescharacteristic
41C23×Dic59C2311yescharacteristic
42C23×Dic59C2312yes—
43C23×Dic59C2311yescharacteristic
44C23×Dic59C2311yescharacteristic
45C23×Dic59C2312yes—
46C22×C4×D59—22no—
47C22×C4×D59—22no—
48C22×C4×D59—22no—
49C22×C4×D59—24no—
50C22×C4×D59—42no—
51C2×Dic59⋊C4—24no—
52C2×Dic59⋊C4—24no—
53C2×Dic59⋊C4—24no—
54C2×Dic59⋊C4—24no—
55C2×Dic59⋊C4—42no—
56C2×Dic59⋊C4C2×C418yescomplemented
57C2×(C2×D59)⋊C4—22no—
58C2×(C2×D59)⋊C4—22no—
59C2×(C2×D59)⋊C4—22no—
60C2×(C2×D59)⋊C4—22no—
61C2×(C2×D59)⋊C4—24no—
62C2×(C2×D59)⋊C4—24no—
63C2×(C2×D59)⋊C4—24no—
64C2×(C2×D59)⋊C4—24no—
65C2×(C2×D59)⋊C4—42no—
66C2×(C2×D59)⋊C4C2×C414yes—
67C2×(C2×D59)⋊C4C2×C418yes—
68C2×(C2×D59)⋊C4Q814yes—
69C2×C4×Dic59—22no—
70C2×C4×Dic59—24no—
71C2×C4×Dic59—24no—
72C2×C4×Dic59—24no—
73C2×C4×Dic59—42no—
74C59⋊#95—22no—
75C59⋊#95—22no—
76C59⋊#95—22no—
77C59⋊#95—24no—
78C59⋊#95—24no—
79C59⋊#95—24no—
80C59⋊#95—24no—
81C59⋊#95C2×C414yescomplemented
82C59⋊#95D418yes—
83C23×C4×C59C2312yes—
84C23×C4×C59C2312yes—
85C23×C4×C59C2311yescharacteristic
86C23×C4×C59C2311yescharacteristic
87C23×C4×C59C2311yescharacteristic
88C2×C4⋊C4×C59—22no—
89C2×C4⋊C4×C59—22no—
90C2×C4⋊C4×C59—22no—
91C2×C4⋊C4×C59—24no—
92C2×C4⋊C4×C59—24no—
93C2×C4⋊C4×C59—24no—
94C2×C4⋊C4×C59—42no—
95C2×C4⋊C4×C59C2×C414yescomplemented
96C2×C42×C59—42no—
97C2×C42×C59D414yes—
98#95×C59—24no—
99C24×C59C2411yescharacteristic
100C23×D59—21no—
101C23×D59—22no—
102C23×D59—21no—
103C23×D59—22no—
104C23×D59—21no—
105C23×D59—21no—
106C23×D59—22no—
107C23×D59—22no—
108C23×D59C22×C412yes—
109C23×D59C2×Q812yes—
110C23×D59#4112yes—
111C22×C4×C59—22no—
112C22×C4×C59—21no—
113C22×C4×C59—21no—
114C22×C4×C59—22no—
115C22×C4×C59—22no—
116C22×C4×C59—22no—
117C22×C4×C59—22no—
118C22×C4×C59—22no—
119C22×C4×C59—22no—
120C22×C4×C59—22no—
121C22×C4×C59—22no—
122C22×C4×C59—22no—
123C22×C4×C59—22no—
124C22×C4×C59—22no—
125C22×C4×C59—22no—
126C22×C4×C59—22no—
127C22×C4×C59—22no—
128C22×C4×C59—22no—
129C22×C4×C59—22no—
130C22×C4×C59—22no—
131C22×C4×C59C22×C414yes—
132C22×C4×C59C22×C412yes—
133C22×C4×C59C2×D412yes—
134C22×C4×C59C2×D412yes—
135C22×C4×C59C2×D414yes—
136C22×C4×C59C2×D412yes—
137C22×C4×C59C2×Q812yes—
138C22×C4×C59#4112yes—
139C22×C4×C59#4112yes—
140C22×Dic59—22no—
141C22×Dic59—22no—
142C22×Dic59—22no—
143C22×Dic59—22no—
144C22×Dic59—22no—
145C22×Dic59—21no—
146C22×Dic59—21no—
147C22×Dic59—21no—
148C22×Dic59—22no—
149C22×Dic59—22no—
150C22×Dic59—22no—
151C22×Dic59—22no—
152C22×Dic59—22no—
153C22×Dic59—21no—
154C22×Dic59—21no—
155C22×Dic59—22no—
156C22×Dic59—22no—
157C22×Dic59—21no—
158C22×Dic59—22no—
159C22×Dic59—22no—
160C22×Dic59—22no—
161C22×Dic59—22no—
162C22×Dic59C22×C412yes—
163C22×Dic59C22×C414yes—
164C22×Dic59C2×D414yes—
165C22×Dic59C2×D414yes—
166C22×Dic59C2×Q812yes—
167C22×Dic59#4112yes—
168C22×Dic59#4114yes—
169C2×C4×D59—28no—
170C2×C4×D59—48no—
171C2×C4×D59—48no—
172C2×C4×D59—44no—
173C2×C4×D59—44no—
174C4⋊C4×C59—28no—
175C4⋊C4×C59—44no—
176C4⋊C4×C59—48no—
177C42×C59—44no—
178(C2×D59)⋊C4—28no—
179(C2×D59)⋊C4—28no—
180(C2×D59)⋊C4—216no—
181(C2×D59)⋊C4—48no—
182Dic59⋊C4—216no—
183Dic59⋊C4—48no—
184C4×Dic59—48no—
185C4×Dic59—44no—
186C23×C59C23×C411yescharacteristic
187C23×C59C22×D412yes—
188C23×C59C22×D411yescharacteristic
189C23×C59C22×Q811yescharacteristic
190C23×C59C2×#4112yes—
191C23×C59C2×#4111yescharacteristic
192C23×C59C2×#4111yescharacteristic
193C23×C59C2×#4111yescharacteristic
194C23×C59C2×#4111yescharacteristic
195C23×C59H(5,𝔽2)12yes—
196C23×C592−1+412yes—
197C22×D59—24no—
198C22×D59—22no—
199C22×D59—22no—
200C22×D59—24no—
201C22×D59—22no—
202C22×D59—22no—
203C22×D59—22no—
204C22×D59—22no—
205C22×D59—24no—
206C22×D59—24no—
207C22×D59—24no—
208C22×D59—24no—
209C22×D59—41no—
210C22×D59—41no—
211C22×D59—42no—
212C22×D59—41no—
213C22×D59—41no—
214C22×D59—42no—
215C22×D59—42no—
216C22×D59—42no—
217C22×D59—42no—
218C22×D59—42no—
219C22×D59C4×Q814yes—
220C2×C4×C59—24no—
221C2×C4×C59—22no—
222C2×C4×C59—22no—
223C2×C4×C59—22no—
224C2×C4×C59—22no—
225C2×C4×C59—22no—
226C2×C4×C59—22no—
227C2×C4×C59—24no—
228C2×C4×C59—24no—
229C2×C4×C59—24no—
230C2×C4×C59—24no—
231C2×C4×C59—24no—
232C2×C4×C59—24no—
233C2×C4×C59—24no—
234C2×C4×C59—24no—
235C2×C4×C59—42no—
236C2×C4×C59—42no—
237C2×C4×C59—42no—
238C2×C4×C59—42no—
239C2×C4×C59—42no—
240C2×C4×C59—42no—
241C2×C4×C59—42no—
242C2×C4×C59—42no—
243C2×C4×C59—42no—
244C2×C4×C59—42no—
245C2×C4×C59—42no—
246C2×C4×C59C4×D414yes—
247C2×C4×C59C22⋊Q814yes—
248C2×C4×C59#12714yes—
249C2×Dic59—24no—
250C2×Dic59—24no—
251C2×Dic59—24no—
252C2×Dic59—24no—
253C2×Dic59—24no—
254C2×Dic59—24no—
255C2×Dic59—24no—
256C2×Dic59—22no—
257C2×Dic59—22no—
258C2×Dic59—22no—
259C2×Dic59—24no—
260C2×Dic59—24no—
261C2×Dic59—24no—
262C2×Dic59—24no—
263C2×Dic59—24no—
264C2×Dic59—42no—
265C2×Dic59—41no—
266C2×Dic59—41no—
267C2×Dic59—41no—
268C2×Dic59—41no—
269C2×Dic59—42no—
270C2×Dic59—41no—
271C2×Dic59—41no—
272C2×Dic59—42no—
273C2×Dic59—42no—
274C2×Dic59—42no—
275C2×Dic59—42no—
276C2×Dic59—42no—
277C2×Dic59C4×D418yes—
278C4×D59—416no—
279#14230—591nomaximal, Sylow
280C22×C59C2×C4×D412yes—
281C22×C59C2×C4×D411yescharacteristic
282C22×C59C2×C4×Q811yescharacteristic
283C22×C59C4×#4111yescharacteristic
284C22×C59#52012yes—
285C22×C59C2×C22⋊Q811yescharacteristic
286C22×C59#52511yescharacteristic
287C22×C59#52911yescharacteristic
288C22×C59C2×#12711yescharacteristic
289C22×C59#53211yescharacteristic
290C22×C59#53212yes—
291C22×C59#53311yescharacteristic
292C22×C59#53411yescharacteristic
293C22×C59#53611yescharacteristic
294C22×C59#53912yes—
295C22×C59#54612yes—
296C22×C59#54612yes—
297C22×C59#54712yes—
298C22×C59D4×Q812yes—
299C22×C59#55112yes—
300C22×C59#55212yes—
301C22×C59#55212yes—
302C22×C59#55412yes—
303C2×D59—28no—
304C2×D59—24no—
305C2×D59—42no—
306C2×D59—42no—
307C2×D59—42no—
308C2×D59—42no—
309C2×D59—44no—
310C2×D59—42no—
311C2×D59—42no—
312C2×D59—44no—
313C2×D59—44no—
314C4×C59—24no—
315C4×C59—24no—
316C4×C59—24no—
317C4×C59—44no—
318C4×C59—82no—
319Dic59—28no—
320Dic59—42no—
321Dic59—42no—
322Dic59—42no—
323Dic59—44no—
324C2×#399—591no—
325C2×#389D5911yescharacteristic, complemented
326C2×#387—592no—
327C2×#385—592no—
328C2×C4×C22⋊C4—591no—
329#1445—591no—
330#1444—591no—
331#1439—591no—
332#1437—592no—
333C4⋊#95—592no—
334C4×#95—591no—
335C2×C59C4×C22⋊Q811yescharacteristic
336C2×C59C4×#12711yescharacteristic
337C2×C59#232211yescharacteristic
338C2×C59#235912yes—
339C2×C59#236012yes—
340C2×C59#253911yescharacteristic
341C2×C59#254211yescharacteristic
342C2×C59#255312yes—
343C2×C59#255612yes—
344C2×C59#256411yescharacteristic
345C2×C59#261111yescharacteristic
346D59—44no—
347C24×C4—591no—
348C22×C4⋊C4—592no—
349C22×C4⋊C4—592no—
350C22×C4⋊C4C2×D5912yes—
351C22×C4⋊C4C2×D5911yescharacteristic
352C22×C4⋊C4C2×D5911yescharacteristic
353C22×C22⋊C4—592no—
354C22×C22⋊C4—591no—
355C22×C22⋊C4—591no—
356C22×C22⋊C4—592no—
357C22×C42—591no—
358C22×C42—592no—
359C22×C42C2×D5911yescharacteristic
360#399—598no—
361#389—24no—
362#387—1188no—
363#385—1188no—
364C4×C22⋊C4—1184no—
365C2×#95—591no—
366C2×#95—592no—
367C2×#95—591no—
368C2×#95—591no—
369C2×#95—592no—
370C2×#95—592no—
371C2×#95—592no—
372C2×#95—592no—
373C2×#95—591no—
374C2×#95C2×D5912yes—
375C59#1423011yescharacteristic, complemented, Sylow
376C25—591no—
377C23×C4—592no—
378C23×C4—591no—
379C23×C4—592no—
380C23×C4—591no—
381C23×C4—591no—
382C23×C4—1182no—
383C23×C4—1182no—
384C23×C4—1182no—
385C23×C4—1184no—
386C23×C4—2362no—
387C23×C4C22×D5912yes—
388C23×C4C22×D5912yes—
389C23×C4C22×D5911yescharacteristic
390C23×C4C22×D5911yescharacteristic
391C23×C4C22×D5911yescharacteristic
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4—598no—
400C2×C4⋊C4—1184no—
401C2×C4⋊C4—1184no—
402C2×C4⋊C4—1184no—
403C2×C4⋊C4—1184no—
404C2×C4⋊C4—2362no—
405C2×C4⋊C4C4×D5914yescomplemented
406C2×C22⋊C4—598no—
407C2×C22⋊C4—594no—
408C2×C22⋊C4—594no—
409C2×C22⋊C4—1184no—
410C2×C22⋊C4—1184no—
411C2×C22⋊C4—1182no—
412C2×C22⋊C4—1182no—
413C2×C22⋊C4—1182no—
414C2×C22⋊C4—1182no—
415C2×C22⋊C4—1184no—
416C2×C22⋊C4—1184no—
417C2×C22⋊C4—2362no—
418C2×C42—42no—
419C2×C42—1184no—
420C2×C42—1184no—
421C2×C42—1184no—
422C2×C42—1182no—
423C2×C42—2362no—
424C2×C42C22⋊D5914yes—
425#95—24no—
426#95—594no—
427#95—598no—
428#95—1184no—
429#95—1184no—
430#95—1184no—
431#95—1184no—
432#95—1182no—
433#95—1182no—
434#95—1182no—
435C24—592no—
436C24—592no—
437C24—592no—
438C24—1182no—
439C24—1181no—
440C24—1182no—
441C24—1181no—
442C24—1181no—
443C24—1181no—
444C24—1182no—
445C24—1182no—
446C24C23×D5911yescharacteristic
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—594no—
468C22×C4—594no—
469C22×C4—594no—
470C22×C4—592no—
471C22×C4—594no—
472C22×C4—592no—
473C22×C4—592no—
474C22×C4—1188no—
475C22×C4—1182no—
476C22×C4—1182no—
477C22×C4—1182no—
478C22×C4—1182no—
479C22×C4—1182no—
480C22×C4—1182no—
481C22×C4—1182no—
482C22×C4—1181no—
483C22×C4—1181no—
484C22×C4—1181no—
485C22×C4—1182no—
486C22×C4—1182no—
487C22×C4—1182no—
488C22×C4—1181no—
489C22×C4—1182no—
490C22×C4—1181no—
491C22×C4—1182no—
492C22×C4—1181no—
493C22×C4—1182no—
494C22×C4—1182no—
495C22×C4—1182no—
496C22×C4—1182no—
497C22×C4—2368no—
498C22×C4—2368no—
499C22×C4—2364no—
500C22×C4—2364no—
501C22×C4C2×C4×D5914yes—
502C22×C4C2×C4×D5912yes—
503C22×C4#1174568512yes—
504C22×C4D4×D5914yes—
505C22×C4Q8×D5912yes—
506C22×C4#1174568912yes—
507C22×C4C2×C22⋊D5912yes—
508C22×C4C2×C22⋊D5912yes—
509C22×C4C2×C22⋊D5912yes—
510C4⋊C4—28no—
511C4⋊C4—44no—
512C4⋊C4—48no—
513C4⋊C4—11816no—
514C4⋊C4—2368no—
515C22⋊C4—11816no—
516C22⋊C4—1188no—
517C22⋊C4—1188no—
518C22⋊C4—2368no—
519C42—44no—
520C42—2368no—
521C42—2364no—
522C23—594no—
523C23—1182no—
524C23—1182no—
525C23—1182no—
526C23—1182no—
527C23—1184no—
528C23—1184no—
529C23—1184no—
530C23—1184no—
531C23—1184no—
532C23—1182no—
533C23—1182no—
534C23—1184no—
535C23—2361no—
536C23—2361no—
537C23—2362no—
538C23—2361no—
539C23—2361no—
540C23—2362no—
541C23—2362no—
542C23—2362no—
543C23—2362no—
544C23—2362no—
545C23C22×C4×D5911yescharacteristic
546C23C2×D4×D5912yes—
547C23C22×C22⋊D5911yescharacteristic
548C23C2×Q8×D5911yescharacteristic
549C23#41×D5911yescharacteristic
550C23#41×D5911yescharacteristic
551C23#41×D5912yes—
552C23C2×#1174568511yescharacteristic
553C23C2×#1174568911yescharacteristic
554C23#1427377212yes—
555C23#1427377512yes—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—598no—
583C2×C4—1184no—
584C2×C4—1184no—
585C2×C4—1184no—
586C2×C4—1184no—
587C2×C4—1184no—
588C2×C4—1184no—
589C2×C4—1182no—
590C2×C4—1182no—
591C2×C4—1184no—
592C2×C4—1184no—
593C2×C4—1184no—
594C2×C4—1184no—
595C2×C4—1184no—
596C2×C4—1184no—
597C2×C4—1182no—
598C2×C4—23616no—
599C2×C4—2362no—
600C2×C4—2361no—
601C2×C4—2361no—
602C2×C4—2361no—
603C2×C4—2361no—
604C2×C4—2362no—
605C2×C4—2361no—
606C2×C4—2361no—
607C2×C4—2362no—
608C2×C4—2362no—
609C2×C4—2362no—
610C2×C4—2362no—
611C2×C4—2362no—
612C2×C4C4×C22⋊D5914yes—
613C2×C4#1427370314yes—
614C2×C4#1427372314yes—
615C22—1188no—
616C22—1184no—
617C22—2362no—
618C22—2362no—
619C22—2362no—
620C22—2362no—
621C22—2362no—
622C22—2364no—
623C22—2364no—
624C22—2364no—
625C22—2362no—
626C22C4×D4×D5912yes—
627C22C2×C4×C22⋊D5911yescharacteristic
628C22C4×Q8×D5911yescharacteristic
629C22C4×#1174568911yescharacteristic
630C22#1683788312yes—
631C22C2×#1427370311yescharacteristic
632C22#1683790911yescharacteristic
633C22#1683793911yescharacteristic
634C22C2×#1427372311yescharacteristic
635C22#1683794811yescharacteristic
636C22#1683794912yes—
637C22#1683795611yescharacteristic
638C22#1683796111yescharacteristic
639C22#1683797611yescharacteristic
640C22#1683799912yes—
641C22#1683804112yes—
642C22#1683804112yes—
643C22#1683805512yes—
644C22#1683806712yes—
645C22#1683807912yes—
646C22#1683808412yes—
647C22#1683808412yes—
648C22#1683810612yes—
649C4—24no—
650C4—24no—
651C4—24no—
652C4—44no—
653C4—82no—
654C4—1188no—
655C4—2362no—
656C4—2362no—
657C4—2364no—
658C4—2362no—
659C2—2364no—
660C2C4×#1427370311yescharacteristic
661C2C4×#1427372311yescharacteristic
662C2#2142676511yescharacteristic
663C2#2142708312yes—
664C2#2142709812yes—
665C2#2142902811yescharacteristic
666C2#2142905011yescharacteristic
667C2#2142914312yes—
668C2#2142918212yes—
669C2#2142927811yescharacteristic
670C2#2142979611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#389C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenterC2×#389D59
hypocenterC59#14230
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#16837283C2semidirect
5. #21422364C2semidirect
6. #21422359C2semidirect
9. Dic59⋊#95C2semidirect
10. C4×C59⋊#95C2semidirect
11. C2×C59×#389C2semidirect
21. #16837337C4semidirect
56. C2×Dic59⋊C4C2×C4semidirect
81. C59⋊#95C2×C4semidirect
95. C2×C4⋊C4×C59C2×C4semidirect
325. C2×#389D59semidirect
375. C59#14230semidirect
405. C2×C4⋊C4C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168373372
C2×#168372832
C2×#168372732
C2×C4×(C2×D59)⋊C42
#214223642
#214223592
#214223382
#214223322
Dic59⋊#952
C4×C59⋊#952
C2×C59×#3892
#1423059