Finite Group Databasebeta

← #28519738

Subgroups — #28519738

Order 15104.

1334 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273717C211yesmaximal, characteristic
2C2×#16837267C211yesmaximal, characteristic
3C2×#16837266C211yesmaximal, characteristic
4#21422362C212yesmaximal
5#21422362C212yesmaximal
6#21422350C211yesmaximal, characteristic
7#21422349C211yesmaximal, characteristic
8#21422348C212yesmaximal
9#21422347C212yesmaximal
10#21422346C211yesmaximal, characteristic
11C59×#1441C211yesmaximal, characteristic
12C2×#14273717—24no—
13C2×#14273717—24no—
14C2×#14273717C418yescomplemented
15C22×C4⋊Dic59C2211yescharacteristic
16C22×C4⋊Dic59C2211yescharacteristic
17C22×Dic59⋊C4C2211yescharacteristic
18C22×Dic59⋊C4C2211yescharacteristic
19C22×Dic59⋊C4C2211yescharacteristic
20C22×Dic59⋊C4C2211yescharacteristic
21C22×Dic59⋊C4C2212yes—
22C22×C4×Dic59C2211yescharacteristic
23#16837267—24no—
24#16837266—24no—
25C2×C59⋊#95C2211yescharacteristic
26C2×C59⋊#95C2212yes—
27C2×C59⋊#95C2212yes—
28C2×C59⋊#95C2212yes—
29C2×C59⋊#95C2212yes—
30C2×C59⋊#95C2212yes—
31C2×C59⋊#95C2212yes—
32C2×C59⋊#95C2212yes—
33C2×C59⋊#95C2212yes—
34C2×C59⋊#95C2212yes—
35C22×C4⋊C4×C59C2211yescharacteristic
36C22×C4⋊C4×C59C2211yescharacteristic
37C2×#95×C59C2211yescharacteristic
38C2×#95×C59C2212yes—
39C2×#95×C59C2212yes—
40C23×Dic59C2312yes—
41C23×Dic59C2312yes—
42C23×Dic59C2311yescharacteristic
43C23×Dic59C2311yescharacteristic
44C23×Dic59C2311yescharacteristic
45C23×Dic59C2311yescharacteristic
46#14273717—232no—
47C2×C4⋊Dic59—22no—
48C2×C4⋊Dic59—22no—
49C2×C4⋊Dic59—22no—
50C2×C4⋊Dic59—42no—
51C2×C4⋊Dic59C2×C414yes—
52C2×Dic59⋊C4—22no—
53C2×Dic59⋊C4—22no—
54C2×Dic59⋊C4—22no—
55C2×Dic59⋊C4—22no—
56C2×Dic59⋊C4—22no—
57C2×Dic59⋊C4—22no—
58C2×Dic59⋊C4—22no—
59C2×Dic59⋊C4—22no—
60C2×Dic59⋊C4—24no—
61C2×Dic59⋊C4—42no—
62C2×Dic59⋊C4—42no—
63C2×Dic59⋊C4C2×C414yes—
64C2×Dic59⋊C4C2×C414yes—
65C2×Dic59⋊C4C2×C414yes—
66C2×Dic59⋊C4C2×C414yes—
67C2×C4×Dic59C2×C414yes—
68C2×C4×Dic59D414yes—
69C2×C4×Dic59D414yes—
70C59⋊#95—22no—
71C59⋊#95—24no—
72C59⋊#95—24no—
73C59⋊#95—24no—
74C59⋊#95—42no—
75C59⋊#95—42no—
76C59⋊#95—42no—
77C59⋊#95—42no—
78C59⋊#95—42no—
79C59⋊#95—42no—
80C23×C4×C59C2312yes—
81C23×C4×C59C2312yes—
82C23×C4×C59C2311yescharacteristic
83C23×C4×C59C2311yescharacteristic
84C23×C4×C59C2311yescharacteristic
85C2×C4⋊C4×C59—22no—
86C2×C4⋊C4×C59—22no—
87C2×C4⋊C4×C59—22no—
88C2×C4⋊C4×C59—42no—
89C2×C4⋊C4×C59C2×C414yes—
90#95×C59—22no—
91#95×C59—42no—
92#95×C59—42no—
93C24×C59C2411yescharacteristic
94C22×C4×C59—22no—
95C22×C4×C59—22no—
96C22×C4×C59—21no—
97C22×C4×C59—21no—
98C22×C4×C59—21no—
99C22×C4×C59—21no—
100C22×C4×C59—21no—
101C22×C4×C59—22no—
102C22×C4×C59—21no—
103C22×C4×C59—21no—
104C22×C4×C59—22no—
105C22×C4×C59—21no—
106C22×C4×C59—22no—
107C22×C4×C59—22no—
108C22×C4×C59—22no—
109C22×C4×C59—22no—
110C22×C4×C59—22no—
111C22×C4×C59—22no—
112C22×C4×C59—22no—
113C22×C4×C59—22no—
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×C59C22×C412yes—
121C22×C4×C59C22×C412yes—
122C22×C4×C59C22×C412yes—
123C22×C4×C59C2×D412yes—
124C22×C4×C59C2×D412yes—
125C22×Dic59—21no—
126C22×Dic59—21no—
127C22×Dic59—22no—
128C22×Dic59—22no—
129C22×Dic59—21no—
130C22×Dic59—21no—
131C22×Dic59—21no—
132C22×Dic59—21no—
133C22×Dic59—21no—
134C22×Dic59—21no—
135C22×Dic59—22no—
136C22×Dic59—21no—
137C22×Dic59—21no—
138C22×Dic59—22no—
139C22×Dic59—21no—
140C22×Dic59—21no—
141C22×Dic59—22no—
142C22×Dic59—22no—
143C22×Dic59—22no—
144C22×Dic59—22no—
145C22×Dic59—22no—
146C22×Dic59—22no—
147C22×Dic59—22no—
148C22×Dic59—22no—
149C22×Dic59—22no—
150C22×Dic59—22no—
151C22×Dic59—22no—
152C22×Dic59—22no—
153C22×Dic59—22no—
154C22×Dic59—22no—
155C22×Dic59C22×C412yes—
156C22×Dic59C22×C412yes—
157C22×Dic59C22×C412yes—
158C22×Dic59C22×C412yes—
159C22×Dic59C2×D412yes—
160C22×Dic59C2×D412yes—
161C22×Dic59C2×D412yes—
162C22×Dic59C2×D412yes—
163C4⋊C4×C59—28no—
164C4⋊C4×C59—44no—
165C4⋊Dic59—28no—
166C4⋊Dic59—44no—
167Dic59⋊C4—28no—
168Dic59⋊C4—28no—
169Dic59⋊C4—28no—
170Dic59⋊C4—28no—
171Dic59⋊C4—48no—
172C4×Dic59C22⋊C4116yes—
173C23×C59C23×C411yescharacteristic
174C23×C59C22×D411yescharacteristic
175C23×C59C22×D411yescharacteristic
176C23×C59H(5,𝔽2)11yescharacteristic
177C23×C59H(5,𝔽2)12yes—
178C23×C59H(5,𝔽2)11yescharacteristic
179C23×C592−1+412yes—
180C23×C592−1+412yes—
181C23×C592−1+411yescharacteristic
182C23×C592−1+412yes—
183C23×C592−1+411yescharacteristic
184C2×C4×C59—24no—
185C2×C4×C59—22no—
186C2×C4×C59—22no—
187C2×C4×C59—24no—
188C2×C4×C59—22no—
189C2×C4×C59—22no—
190C2×C4×C59—24no—
191C2×C4×C59—22no—
192C2×C4×C59—22no—
193C2×C4×C59—41no—
194C2×C4×C59—41no—
195C2×C4×C59—41no—
196C2×C4×C59—41no—
197C2×C4×C59—42no—
198C2×C4×C59—41no—
199C2×C4×C59—41no—
200C2×C4×C59—42no—
201C2×C4×C59—42no—
202C2×C4×C59—42no—
203C2×C4×C59—42no—
204C2×C4×C59—42no—
205C2×C4×C59—42no—
206C2×C4×C59—42no—
207C2×C4×C59—42no—
208C2×C4×C59—42no—
209C2×C4×C59—42no—
210C2×C4×C59—42no—
211C2×C4×C59—42no—
212C2×C4×C59—42no—
213C2×C4×C59—42no—
214C2×C4×C59C2×C22⋊C414yes—
215C2×Dic59—24no—
216C2×Dic59—22no—
217C2×Dic59—22no—
218C2×Dic59—22no—
219C2×Dic59—22no—
220C2×Dic59—24no—
221C2×Dic59—22no—
222C2×Dic59—22no—
223C2×Dic59—22no—
224C2×Dic59—22no—
225C2×Dic59—22no—
226C2×Dic59—22no—
227C2×Dic59—24no—
228C2×Dic59—22no—
229C2×Dic59—22no—
230C2×Dic59—41no—
231C2×Dic59—41no—
232C2×Dic59—41no—
233C2×Dic59—41no—
234C2×Dic59—42no—
235C2×Dic59—41no—
236C2×Dic59—41no—
237C2×Dic59—42no—
238C2×Dic59—42no—
239C2×Dic59—42no—
240C2×Dic59—42no—
241C2×Dic59—42no—
242C2×Dic59—42no—
243C2×Dic59—42no—
244C2×Dic59—42no—
245C2×Dic59—42no—
246C2×Dic59—42no—
247C2×Dic59—42no—
248C2×Dic59—42no—
249C2×Dic59—42no—
250C2×Dic59—42no—
251C2×Dic59C2×C22⋊C414yes—
252C2×Dic59C2×C22⋊C414yes—
253#14664—591nomaximal, Sylow
254C22×C59C22×C22⋊C411yescharacteristic
255C22×C59#51912yes—
256C22×C59#52012yes—
257C22×C59#52011yescharacteristic
258C22×C59#52011yescharacteristic
259C22×C59#53511yescharacteristic
260C22×C59#53511yescharacteristic
261C22×C59#53611yescharacteristic
262C22×C59#53611yescharacteristic
263C22×C59#53612yes—
264C22×C59#53611yescharacteristic
265C22×C59#53611yescharacteristic
266C22×C59#53712yes—
267C22×C59#53711yescharacteristic
268C22×C59#53711yescharacteristic
269C22×C59#56212yes—
270C22×C59#56212yes—
271C22×C59#56312yes—
272C22×C59#56312yes—
273C22×C59#56312yes—
274C22×C59#56312yes—
275C22×C59#56412yes—
276C22×C59#56412yes—
277C4×C59—24no—
278C4×C59—42no—
279C4×C59—42no—
280C4×C59—82no—
281C4×C59—82no—
282Dic59—24no—
283Dic59—24no—
284Dic59—42no—
285Dic59—42no—
286Dic59—82no—
287Dic59—82no—
288C22×#125—591no—
289C2×#382—591no—
290C2×#382—591no—
291#1445—592no—
292#1445—592no—
293#1441—592no—
294#1441—592no—
295#1441—591no—
296#1441—591no—
297#1441—591no—
298#1441D5911yescharacteristic
299C2×C59#231011yescharacteristic
300C2×C59#231111yescharacteristic
301C2×C59#231111yescharacteristic
302C2×C59#238212yes—
303C2×C59#238212yes—
304C2×C59#282012yes—
305C2×C59#282011yescharacteristic
306C2×C59#282011yescharacteristic
307C2×C59#282212yes—
308C2×C59#282211yescharacteristic
309C2×C59#282211yescharacteristic
310C2×#125—598no—
311C2×#125—1184no—
312C2×#125—1184no—
313C22×C4⋊C4—591no—
314C22×C4⋊C4—591no—
315C22×C4⋊C4—591no—
316C22×C4⋊C4—591no—
317C22×C4⋊C4—591no—
318C22×C4⋊C4—592no—
319C22×C4⋊C4—591no—
320C22×C4⋊C4C2×D5911yescharacteristic
321C22×C4⋊C4C2×D5911yescharacteristic
322C22×C42—591no—
323#382—1184no—
324#382—1184no—
325C2×#95—592no—
326C2×#95—591no—
327C2×#95—592no—
328C2×#95—592no—
329C2×#95—592no—
330C2×#95—592no—
331C2×#95—592no—
332C2×#95—592no—
333C2×#95—592no—
334C2×#95—592no—
335C2×#95C2×D5911yescharacteristic
336C2×#95C2×D5912yes—
337C2×#95C2×D5912yes—
338C59#1466411yescharacteristic, complemented, Sylow
339C23×C4—591no—
340C23×C4—591no—
341C23×C4—591no—
342C23×C4—591no—
343C23×C4—592no—
344C23×C4—592no—
345C23×C4C22×D5912yes—
346C23×C4C22×D5912yes—
347C23×C4C22×D5911yescharacteristic
348C23×C4C22×D5911yescharacteristic
349C23×C4C22×D5911yescharacteristic
350#125—11832no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—594no—
356C2×C4⋊C4—594no—
357C2×C4⋊C4—594no—
358C2×C4⋊C4—594no—
359C2×C4⋊C4—594no—
360C2×C4⋊C4—1182no—
361C2×C4⋊C4—1182no—
362C2×C4⋊C4—1182no—
363C2×C4⋊C4—1182no—
364C2×C4⋊C4—1182no—
365C2×C4⋊C4—1182no—
366C2×C4⋊C4—1182no—
367C2×C4⋊C4—1182no—
368C2×C4⋊C4—1182no—
369C2×C4⋊C4—1182no—
370C2×C4⋊C4—1184no—
371C2×C4⋊C4—1182no—
372C2×C4⋊C4—2362no—
373C2×C4⋊C4—2362no—
374C2×C4⋊C4—2362no—
375C2×C4⋊C4C4×D5914yes—
376C2×C42—594no—
377C2×C42—594no—
378C2×C42—594no—
379#95—22no—
380#95—42no—
381#95—42no—
382#95—1184no—
383#95—1184no—
384#95—1184no—
385#95—1182no—
386#95—2362no—
387#95—2362no—
388#95—2362no—
389#95—2362no—
390#95—2362no—
391#95—2362no—
392C24C23×D5911yescharacteristic
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—592no—
420C22×C4—592no—
421C22×C4—592no—
422C22×C4—592no—
423C22×C4—592no—
424C22×C4—592no—
425C22×C4—592no—
426C22×C4—592no—
427C22×C4—1181no—
428C22×C4—1181no—
429C22×C4—1182no—
430C22×C4—1181no—
431C22×C4—1182no—
432C22×C4—1181no—
433C22×C4—1181no—
434C22×C4—1181no—
435C22×C4—1181no—
436C22×C4—1181no—
437C22×C4—1182no—
438C22×C4—1181no—
439C22×C4—1181no—
440C22×C4—1182no—
441C22×C4—1181no—
442C22×C4—1181no—
443C22×C4—1182no—
444C22×C4—1182no—
445C22×C4—1182no—
446C22×C4—1182no—
447C22×C4—1182no—
448C22×C4—1182no—
449C22×C4—1182no—
450C22×C4—1182no—
451C22×C4—1182no—
452C22×C4—1182no—
453C22×C4—1182no—
454C22×C4—1182no—
455C22×C4—1182no—
456C22×C4—1182no—
457C22×C4C2×C4×D5912yes—
458C22×C4C2×C4×D5912yes—
459C22×C4C2×C4×D5912yes—
460C22×C4D4×D5912yes—
461C22×C4D4×D5912yes—
462C4⋊C4—28no—
463C4⋊C4—44no—
464C4⋊C4—1188no—
465C4⋊C4—1188no—
466C4⋊C4—1188no—
467C4⋊C4—1188no—
468C4⋊C4—1188no—
469C4⋊C4—2364no—
470C4⋊C4—2368no—
471C42—5916no—
472C23C22×C4×D5911yescharacteristic
473C23C2×D4×D5911yescharacteristic
474C23C2×D4×D5911yescharacteristic
475C23#1427377211yescharacteristic
476C23#1427377212yes—
477C23#1427377311yescharacteristic
478C23#1427377412yes—
479C23#1427377412yes—
480C23#1427377411yescharacteristic
481C23#1427377512yes—
482C23#1427377511yescharacteristic
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—594no—
514C2×C4—594no—
515C2×C4—1182no—
516C2×C4—1182no—
517C2×C4—1184no—
518C2×C4—1182no—
519C2×C4—1182no—
520C2×C4—1182no—
521C2×C4—1182no—
522C2×C4—1184no—
523C2×C4—1182no—
524C2×C4—1182no—
525C2×C4—1182no—
526C2×C4—1182no—
527C2×C4—1184no—
528C2×C4—1182no—
529C2×C4—1182no—
530C2×C4—2362no—
531C2×C4—2362no—
532C2×C4—2362no—
533C2×C4—2362no—
534C2×C4—2362no—
535C2×C4—2362no—
536C2×C4—2362no—
537C2×C4—2362no—
538C2×C4—2362no—
539C2×C4—2362no—
540C2×C4—2362no—
541C2×C4—2362no—
542C2×C4—2362no—
543C2×C4—2362no—
544C2×C4—2361no—
545C2×C4—2361no—
546C2×C4—2361no—
547C2×C4—2361no—
548C2×C4—2362no—
549C2×C4—2361no—
550C2×C4—2361no—
551C2×C4C22⋊C4×D5914yes—
552C22C2×C22⋊C4×D5911yescharacteristic
553C22#1683787812yes—
554C22#1683788112yes—
555C22#1683788211yescharacteristic
556C22#1683788311yescharacteristic
557C22#1683796711yescharacteristic
558C22#1683796811yescharacteristic
559C22#1683797211yescharacteristic
560C22#1683797411yescharacteristic
561C22#1683797512yes—
562C22#1683797511yescharacteristic
563C22#1683797711yescharacteristic
564C22#1683797912yes—
565C22#1683798111yescharacteristic
566C22#1683798211yescharacteristic
567C22#1683814712yes—
568C22#1683814812yes—
569C22#1683815112yes—
570C22#1683815312yes—
571C22#1683815412yes—
572C22#1683815512yes—
573C22C59⋊#56412yes—
574C22C59⋊#56412yes—
575C4—24no—
576C4—42no—
577C4—42no—
578C4—82no—
579C4—82no—
580C4—1184no—
581C4—1184no—
582C4—4722no—
583C4—4722no—
584C4—2362no—
585C4—2362no—
586C2#2142667911yescharacteristic
587C2#2142668311yescharacteristic
588C2#2142668511yescharacteristic
589C2#2142727812yes—
590C2#2142728012yes—
591C2#2143214512yes—
592C2#2143214911yescharacteristic
593C2#2143215111yescharacteristic
594C2#2143216212yes—
595C2#2143216511yescharacteristic
596C2#2143216611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×#1441C2
socle, prime radical, cosocleC24×C59C24
hypercenter#1441D59
hypocenterC59#14664
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
14. C2×#14273717C4semidirect
338. C59#14664semidirect

Maximal subgroups

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

subgroupindex
C22×#142737172
C2×#168372672
C2×#168372662
#214223622
#214223502
#214223492
#214223482
#214223472
#214223462
C59×#14412
#1466459