Finite Group Databasebeta

← #28525411

Subgroups — #28525411

Order 15104.

1566 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837334C211yesmaximal, characteristic
2C2×#16837333C211yesmaximal, characteristic
3C2×#16837332C211yesmaximal, characteristic
4C2×#16837297C211yesmaximal, characteristic
5C2×#16837271C212yesmaximal
6C2×#16837271C211yesmaximal, characteristic
7#21422360C212yesmaximal
8#21422359C212yesmaximal
9Dic59⋊#95C212yesmaximal
10#95×Dic59C211yesmaximal, characteristic
11C2×C59×#398C211yesmaximal, characteristic
12C22×C4⋊Dic59C2211yescharacteristic
13C22×C4⋊Dic59C2212yes—
14C22×Dic59⋊C4C2212yes—
15C22×Dic59⋊C4C2211yescharacteristic
16C22×Dic59⋊C4C2211yescharacteristic
17C22×Dic59⋊C4C2212yes—
18C22×Dic59⋊C4C2212yes—
19C22×Dic59⋊C4C2211yescharacteristic
20C22×Dic59⋊C4C2212yes—
21C22×C4×Dic59C2211yescharacteristic
22C22×C4×Dic59C2212yes—
23#16837334—24no—
24#16837333—24no—
25#16837332—24no—
26#16837297—24no—
27#16837271—28no—
28#16837271—24no—
29C2×C59⋊#95C2211yescharacteristic
30C2×C59⋊#95C2212yes—
31C2×C59⋊#95C2212yes—
32C2×C59⋊#95C2211yescharacteristic
33C2×C59⋊#95C2212yes—
34C2×C59⋊#95C2211yescharacteristic
35C2×C59⋊#95C2212yes—
36C22×C4⋊C4×C59C2211yescharacteristic
37C22×C4⋊C4×C59C2211yescharacteristic
38C22×C4⋊C4×C59C2212yes—
39C59×#398—24no—
40C2×#95×C59C2212yes—
41C2×#95×C59C2211yescharacteristic
42C23×Dic59C2311yescharacteristic
43C23×Dic59C2312yes—
44C23×Dic59C2311yescharacteristic
45C23×Dic59C2312yes—
46C23×Dic59C2311yescharacteristic
47C23×Dic59C2311yescharacteristic
48C2×C4⋊Dic59—22no—
49C2×C4⋊Dic59—22no—
50C2×C4⋊Dic59—24no—
51C2×C4⋊Dic59—22no—
52C2×C4⋊Dic59—24no—
53C2×C4⋊Dic59—42no—
54C2×Dic59⋊C4—22no—
55C2×Dic59⋊C4—22no—
56C2×Dic59⋊C4—24no—
57C2×Dic59⋊C4—22no—
58C2×Dic59⋊C4—22no—
59C2×Dic59⋊C4—22no—
60C2×Dic59⋊C4—24no—
61C2×Dic59⋊C4—24no—
62C2×Dic59⋊C4—24no—
63C2×Dic59⋊C4—24no—
64C2×Dic59⋊C4—22no—
65C2×Dic59⋊C4—24no—
66C2×Dic59⋊C4—24no—
67C2×Dic59⋊C4—24no—
68C2×Dic59⋊C4—24no—
69C2×Dic59⋊C4—42no—
70C2×Dic59⋊C4—42no—
71C2×Dic59⋊C4—42no—
72C2×Dic59⋊C4—42no—
73C2×Dic59⋊C4D414yes—
74C2×C4×Dic59—24no—
75C2×C4×Dic59—24no—
76C2×C4×Dic59—24no—
77C2×C4×Dic59D414yes—
78C2×C4×Dic59Q818yes—
79C59⋊#95—24no—
80C59⋊#95—22no—
81C59⋊#95—22no—
82C59⋊#95—24no—
83C59⋊#95—24no—
84C59⋊#95D414yes—
85C59⋊#95Q818yes—
86C23×C4×C59C2311yescharacteristic
87C23×C4×C59C2312yes—
88C23×C4×C59C2311yescharacteristic
89C23×C4×C59C2311yescharacteristic
90C23×C4×C59C2312yes—
91C2×C4⋊C4×C59—24no—
92C2×C4⋊C4×C59—22no—
93C2×C4⋊C4×C59—22no—
94C2×C4⋊C4×C59—24no—
95C2×C4⋊C4×C59—22no—
96C2×C4⋊C4×C59—22no—
97C2×C4⋊C4×C59—22no—
98C2×C4⋊C4×C59—22no—
99C2×C4⋊C4×C59—42no—
100#95×C59—24no—
101#95×C59D414yes—
102C24×C59C2411yescharacteristic
103C22×C4×C59—22no—
104C22×C4×C59—22no—
105C22×C4×C59—22no—
106C22×C4×C59—22no—
107C22×C4×C59—22no—
108C22×C4×C59—22no—
109C22×C4×C59—21no—
110C22×C4×C59—21no—
111C22×C4×C59—21no—
112C22×C4×C59—21no—
113C22×C4×C59—21no—
114C22×C4×C59—21no—
115C22×C4×C59—21no—
116C22×C4×C59—22no—
117C22×C4×C59—21no—
118C22×C4×C59—21no—
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×C59C2×D412yes—
128C22×C4×C59C2×D412yes—
129C22×C4×C59C2×D412yes—
130C22×C4×C59C2×D412yes—
131C22×C4×C59C2×D414yes—
132C22×C4×C59C2×Q814yes—
133C22×C4×C59C2×Q814yes—
134C22×Dic59—22no—
135C22×Dic59—22no—
136C22×Dic59—22no—
137C22×Dic59—21no—
138C22×Dic59—21no—
139C22×Dic59—22no—
140C22×Dic59—22no—
141C22×Dic59—21no—
142C22×Dic59—21no—
143C22×Dic59—21no—
144C22×Dic59—21no—
145C22×Dic59—21no—
146C22×Dic59—21no—
147C22×Dic59—21no—
148C22×Dic59—21no—
149C22×Dic59—21no—
150C22×Dic59—22no—
151C22×Dic59—22no—
152C22×Dic59—22no—
153C22×Dic59—22no—
154C22×Dic59—22no—
155C22×Dic59—22no—
156C22×Dic59—22no—
157C22×Dic59—22no—
158C22×Dic59—22no—
159C22×Dic59C2×D412yes—
160C22×Dic59C2×D414yes—
161C22×Dic59C2×D412yes—
162C22×Dic59C2×D412yes—
163C22×Dic59C2×D412yes—
164C22×Dic59C2×Q814yes—
165C22×Dic59C2×Q814yes—
166C22×Dic59C2×Q814yes—
167C22×Dic59C2×Q814yes—
168C22×Dic59#4112yes—
169C22×Dic59#4114yes—
170C4⋊C4×C59—48no—
171C4⋊C4×C59—44no—
172C4⋊C4×C59—44no—
173C4⋊Dic59—48no—
174C4⋊Dic59—44no—
175Dic59⋊C4—28no—
176Dic59⋊C4—48no—
177Dic59⋊C4—48no—
178Dic59⋊C4—48no—
179Dic59⋊C4—44no—
180Dic59⋊C4—48no—
181Dic59⋊C4—44no—
182C4×Dic59—216no—
183C4×Dic59—28no—
184C23×C59C22×D411yescharacteristic
185C23×C59C22×D411yescharacteristic
186C23×C59C22×D411yescharacteristic
187C23×C59C22×D411yescharacteristic
188C23×C59C22×Q812yes—
189C23×C59C22×Q812yes—
190C23×C59C2×#4111yescharacteristic
191C23×C59C2×#4112yes—
192C23×C59H(5,𝔽2)11yescharacteristic
193C23×C59H(5,𝔽2)11yescharacteristic
194C23×C592−1+412yes—
195C2×C4×C59—24no—
196C2×C4×C59—22no—
197C2×C4×C59—22no—
198C2×C4×C59—24no—
199C2×C4×C59—24no—
200C2×C4×C59—24no—
201C2×C4×C59—24no—
202C2×C4×C59—24no—
203C2×C4×C59—24no—
204C2×C4×C59—24no—
205C2×C4×C59—22no—
206C2×C4×C59—22no—
207C2×C4×C59—22no—
208C2×C4×C59—41no—
209C2×C4×C59—41no—
210C2×C4×C59—41no—
211C2×C4×C59—41no—
212C2×C4×C59—42no—
213C2×C4×C59—41no—
214C2×C4×C59—41no—
215C2×C4×C59—42no—
216C2×C4×C59—42no—
217C2×C4×C59—41no—
218C2×C4×C59—42no—
219C2×C4×C59—42no—
220C2×C4×C59—42no—
221C2×C4×C59—42no—
222C2×C4×C59—42no—
223C2×C4×C59—42no—
224C2×C4×C59#12714yes—
225C2×C4×C59C4⋊Q818yes—
226C2×Dic59—24no—
227C2×Dic59—22no—
228C2×Dic59—22no—
229C2×Dic59—24no—
230C2×Dic59—24no—
231C2×Dic59—24no—
232C2×Dic59—24no—
233C2×Dic59—24no—
234C2×Dic59—24no—
235C2×Dic59—24no—
236C2×Dic59—22no—
237C2×Dic59—22no—
238C2×Dic59—22no—
239C2×Dic59—41no—
240C2×Dic59—41no—
241C2×Dic59—41no—
242C2×Dic59—41no—
243C2×Dic59—42no—
244C2×Dic59—41no—
245C2×Dic59—41no—
246C2×Dic59—42no—
247C2×Dic59—42no—
248C2×Dic59—41no—
249C2×Dic59—42no—
250C2×Dic59—42no—
251C2×Dic59—42no—
252C2×Dic59—42no—
253C2×Dic59—42no—
254C2×Dic59—42no—
255C2×Dic59#12114yes—
256C2×Dic59C22⋊Q818yes—
257C2×Dic59#12314yes—
258C2×Dic59#12518yes—
259C2×Dic59C4⋊Q818yes—
260C2×Dic59C4⋊Q814yes—
261C2×Dic59C4⋊Q814yes—
262#15145—591nomaximal, Sylow
263C22×C59C2×#12111yescharacteristic
264C22×C59C2×C22⋊Q812yes—
265C22×C59C2×#12311yescharacteristic
266C22×C59C2×#12512yes—
267C22×C59C2×#12711yescharacteristic
268C22×C59C2×C4⋊Q811yescharacteristic
269C22×C59C2×C4⋊Q812yes—
270C22×C59C2×C4⋊Q811yescharacteristic
271C22×C59C2×C4⋊Q812yes—
272C22×C59#53511yescharacteristic
273C22×C59#53611yescharacteristic
274C22×C59#54412yes—
275C22×C59#54412yes—
276C22×C59D4211yescharacteristic
277C22×C59D4211yescharacteristic
278C22×C59#54712yes—
279C22×C59#54712yes—
280C22×C59D4×Q812yes—
281C22×C59#55011yescharacteristic
282C22×C59#55011yescharacteristic
283C22×C59#55412yes—
284C22×C59#55412yes—
285C22×C59#55712yes—
286C4×C59—28no—
287C4×C59—24no—
288C4×C59—42no—
289C4×C59—81no—
290C4×C59—82no—
291Dic59—28no—
292Dic59—24no—
293Dic59—42no—
294Dic59—81no—
295Dic59—82no—
296Dic59#39818yescomplemented
297C2×#398—591no—
298C2×#398—591no—
299C2×#398—591no—
300C2×#398D5911yescharacteristic
301C2×#389—591no—
302C2×#384—592no—
303C2×#384—591no—
304#1444—592no—
305#1444—592no—
306C4⋊#95—592no—
307C4×#95—591no—
308C2×C59C2×#39811yescharacteristic
309C2×C59#244012yes—
310C2×C59#244012yes—
311C2×C59#250111yescharacteristic
312C2×C59#250211yescharacteristic
313C2×C59#254111yescharacteristic
314C2×C59#254611yescharacteristic
315C2×C59#255212yes—
316C2×C59#255212yes—
317C2×C59#266011yescharacteristic
318C2×C59#286811yescharacteristic
319C22×C4⋊C4—591no—
320C22×C4⋊C4—591no—
321C22×C4⋊C4—591no—
322C22×C4⋊C4—591no—
323C22×C4⋊C4—592no—
324C22×C4⋊C4—592no—
325C22×C4⋊C4—592no—
326C22×C4⋊C4—592no—
327C22×C4⋊C4—592no—
328C22×C4⋊C4C2×D5911yescharacteristic
329C22×C4⋊C4C2×D5911yescharacteristic
330C22×C4⋊C4C2×D5912yes—
331C22×C42—592no—
332C22×C42—591no—
333#398—24no—
334#398—1184no—
335#398—1184no—
336#398—1184no—
337#389—1184no—
338#384—1184no—
339#384—1188no—
340C2×#95—591no—
341C2×#95—592no—
342C2×#95—592no—
343C2×#95—592no—
344C2×#95—592no—
345C2×#95—591no—
346C2×#95—591no—
347C2×#95C2×D5912yes—
348C2×#95C2×D5911yescharacteristic
349C59#1514511yescharacteristic, complemented, Sylow
350C23×C4—591no—
351C23×C4—592no—
352C23×C4—591no—
353C23×C4—591no—
354C23×C4—592no—
355C23×C4—591no—
356C23×C4C22×D5912yes—
357C23×C4C22×D5911yescharacteristic
358C23×C4C22×D5911yescharacteristic
359C23×C4C22×D5911yescharacteristic
360C23×C4C22×D5912yes—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—594no—
371C2×C4⋊C4—1182no—
372C2×C4⋊C4—1182no—
373C2×C4⋊C4—1184no—
374C2×C4⋊C4—1184no—
375C2×C4⋊C4—1184no—
376C2×C4⋊C4—1184no—
377C2×C4⋊C4—1184no—
378C2×C4⋊C4—1182no—
379C2×C4⋊C4—1184no—
380C2×C4⋊C4—1184no—
381C2×C4⋊C4—1184no—
382C2×C4⋊C4—1184no—
383C2×C4⋊C4—1184no—
384C2×C4⋊C4—1182no—
385C2×C4⋊C4—1182no—
386C2×C4⋊C4—1182no—
387C2×C4⋊C4—1182no—
388C2×C4⋊C4—1182no—
389C2×C4⋊C4—1184no—
390C2×C4⋊C4—1182no—
391C2×C4⋊C4—2362no—
392C2×C4⋊C4—2362no—
393C2×C4⋊C4—2362no—
394C2×C4⋊C4—2362no—
395C2×C4⋊C4—2362no—
396C2×C42—594no—
397C2×C42—598no—
398C2×C42—1184no—
399C2×C42—1184no—
400C2×C42—1184no—
401#95—24no—
402#95—594no—
403#95—598no—
404#95—1182no—
405#95—1182no—
406#95—1184no—
407#95—1184no—
408#95—1184no—
409#95C22⋊D5914yes—
410C24C23×D5911yescharacteristic
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—592no—
436C22×C4—592no—
437C22×C4—594no—
438C22×C4—594no—
439C22×C4—592no—
440C22×C4—594no—
441C22×C4—592no—
442C22×C4—594no—
443C22×C4—594no—
444C22×C4—594no—
445C22×C4—592no—
446C22×C4—1182no—
447C22×C4—1182no—
448C22×C4—1182no—
449C22×C4—1181no—
450C22×C4—1181no—
451C22×C4—1182no—
452C22×C4—1182no—
453C22×C4—1181no—
454C22×C4—1181no—
455C22×C4—1181no—
456C22×C4—1181no—
457C22×C4—1181no—
458C22×C4—1181no—
459C22×C4—1181no—
460C22×C4—1181no—
461C22×C4—1182no—
462C22×C4—1182no—
463C22×C4—1182no—
464C22×C4—1181no—
465C22×C4—1182no—
466C22×C4—1182no—
467C22×C4—1182no—
468C22×C4—1182no—
469C22×C4—1182no—
470C22×C4—1182no—
471C22×C4D4×D5912yes—
472C22×C4D4×D5912yes—
473C22×C4D4×D5912yes—
474C22×C4Q8×D5914yes—
475C22×C4Q8×D5914yes—
476C22×C4C2×C22⋊D5912yes—
477C22×C4C2×C22⋊D5914yes—
478C4⋊C4—48no—
479C4⋊C4—44no—
480C4⋊C4—44no—
481C4⋊C4—1188no—
482C4⋊C4—2368no—
483C4⋊C4—2368no—
484C4⋊C4—2368no—
485C4⋊C4—2364no—
486C4⋊C4—2368no—
487C4⋊C4—2368no—
488C4⋊C4—2364no—
489C4⋊C4—2364no—
490C42—11816no—
491C42—1188no—
492C23C2×D4×D5911yescharacteristic
493C23C2×D4×D5911yescharacteristic
494C23C2×D4×D5911yescharacteristic
495C23C22×C22⋊D5911yescharacteristic
496C23C2×Q8×D5912yes—
497C23C2×Q8×D5912yes—
498C23#41×D5911yescharacteristic
499C23#41×D5912yes—
500C23#1427377211yescharacteristic
501C23#1427377311yescharacteristic
502C23#1427377412yes—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—594no—
533C2×C4—598no—
534C2×C4—594no—
535C2×C4—598no—
536C2×C4—594no—
537C2×C4—598no—
538C2×C4—594no—
539C2×C4—1184no—
540C2×C4—1182no—
541C2×C4—1182no—
542C2×C4—1184no—
543C2×C4—1184no—
544C2×C4—1184no—
545C2×C4—1184no—
546C2×C4—1184no—
547C2×C4—1184no—
548C2×C4—1184no—
549C2×C4—1182no—
550C2×C4—1182no—
551C2×C4—1182no—
552C2×C4—2362no—
553C2×C4—2361no—
554C2×C4—2362no—
555C2×C4—2361no—
556C2×C4—2362no—
557C2×C4—2361no—
558C2×C4—2362no—
559C2×C4—2362no—
560C2×C4—2362no—
561C2×C4—2362no—
562C2×C4—2362no—
563C2×C4—2362no—
564C2×C4—2361no—
565C2×C4—2361no—
566C2×C4—2361no—
567C2×C4—2361no—
568C2×C4#1427372314yes—
569C2×C4#1427372518yes—
570C22#121×D5911yescharacteristic
571C22C22⋊Q8×D5912yes—
572C22#123×D5911yescharacteristic
573C22#125×D5912yes—
574C22C2×#1427372311yescharacteristic
575C22C4⋊Q8×D5912yes—
576C22C4⋊Q8×D5911yescharacteristic
577C22C4⋊Q8×D5911yescharacteristic
578C22C2×#1427372512yes—
579C22#1683796811yescharacteristic
580C22#1683797411yescharacteristic
581C22#1683803112yes—
582C22#1683803212yes—
583C22D4×C22⋊D5911yescharacteristic
584C22#1683803611yescharacteristic
585C22#1683805012yes—
586C22#1683805112yes—
587C22#1683806512yes—
588C22#1683807011yescharacteristic
589C22#1683807111yescharacteristic
590C22#1683810612yes—
591C22#1683810812yes—
592C22#1683812912yes—
593C4—28no—
594C4—24no—
595C4—42no—
596C4—82no—
597C4—81no—
598C4—598no—
599C4—1188no—
600C4—1184no—
601C4—4722no—
602C4—4721no—
603C4—2362no—
604C2#398×D5911yescharacteristic
605C2#2142779312yes—
606C2#2142779512yes—
607C2#2142856511yescharacteristic
608C2#2142856911yescharacteristic
609C2#2142903911yescharacteristic
610C2#2142908011yescharacteristic
611C2#2142912612yes—
612C2#2142912812yes—
613C2#2143021911yescharacteristic
614C2#2143249211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutator, socle, prime radical, cosocleC24×C59C24
FittingC2×C59×#398C2
hypercenterC2×#398D59
hypocenterC59#15145
LCSG ▷ C24×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
296. Dic59#398semidirect
349. C59#15145semidirect

Maximal subgroups

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

subgroupindex
C2×#168373342
C2×#168373332
C2×#168373322
C2×#168372972
C2×#168372712
#214223602
#214223592
Dic59⋊#952
#95×Dic592
C2×C59×#3982
#1514559