Finite Group Databasebeta

← #28517086

Subgroups — #28517086

Order 15104.

2018 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837304C211yesmaximal, characteristic
2C2×#16837280C212yesmaximal
3C2×#16837276C212yesmaximal, complemented
4#21422348C212yesmaximal, complemented
5#21422342C212yesmaximal, complemented
6#21422340C212yesmaximal, complemented
7#21422326C211yesmaximal, characteristic, complemented
8(C2×D59)⋊#95C212yesmaximal, complemented
9C59×#1434C211yesmaximal, characteristic, complemented
10C23×D236C2211yescharacteristic
11C23×C4×D59C2212yes—
12C22×C4⋊Dic59C2212yes—
13C22×C4⋊Dic59C2211yescharacteristic
14C22×Dic59⋊C4C2212yes—
15C22×(C2×D59)⋊C4C2212yes—
16C22×(C2×D59)⋊C4C2212yes—
17C22×(C2×D59)⋊C4C2212yes—
18C22×(C2×D59)⋊C4C2212yes—
19C22×(C2×D59)⋊C4C2212yes—
20#16837304C418yescomplemented
21#16837280—28no—
22#16837276—28no—
23C2×C59⋊#95C2212yes—
24C2×C59⋊#95C2212yes—
25C2×C59⋊#95C2211yescharacteristic
26C2×C59⋊#95C2212yes—
27C2×C59⋊#95C2212yes—
28C2×C59⋊#95C2211yescharacteristic
29C22×C42×C59C2211yescharacteristic
30C2×#95×C59C2211yescharacteristic
31C2×#95×C59C2212yes—
32C2×#95×C59C2212yes—
33C2×#95×C59C2211yescharacteristic
34C24×D59C2312yes—
35C22×D236—42no—
36C22×D236—42no—
37C22×D236C2×C414yes—
38C22×D236D414yes—
39C22×D236Q814yes—
40C23×Dic59C2312yes—
41C23×Dic59C2312yes—
42C23×Dic59C2312yes—
43C22×C4×D59—24no—
44C22×C4×D59—24no—
45C22×C4×D59—24no—
46C22×C4×D59—42no—
47C22×C4×D59—42no—
48C22×C4×D59—42no—
49C22×C4×D59—42no—
50C2×C4⋊Dic59—24no—
51C2×C4⋊Dic59—24no—
52C2×C4⋊Dic59—42no—
53C2×C4⋊Dic59—42no—
54C2×C4⋊Dic59C2×C414yescomplemented
55C2×Dic59⋊C4—24no—
56C2×Dic59⋊C4—42no—
57C2×Dic59⋊C4—42no—
58C2×(C2×D59)⋊C4—24no—
59C2×(C2×D59)⋊C4—24no—
60C2×(C2×D59)⋊C4—24no—
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)⋊C4—42no—
67C2×(C2×D59)⋊C4—42no—
68C2×(C2×D59)⋊C4—42no—
69C2×(C2×D59)⋊C4—42no—
70C2×(C2×D59)⋊C4—42no—
71C2×(C2×D59)⋊C4C2×C418yescomplemented
72C2×(C2×D59)⋊C4C2×C418yescomplemented
73C59⋊#95—24no—
74C59⋊#95—24no—
75C59⋊#95—42no—
76C59⋊#95—42no—
77C59⋊#95—41no—
78C59⋊#95—41no—
79C23×C4×C59C2312yes—
80C23×C4×C59C2311yescharacteristic
81C23×C4×C59C2312yes—
82C23×C4×C59C2311yescharacteristic
83C23×C4×C59C2311yescharacteristic
84C2×C42×C59—42no—
85C2×C42×C59C2×C414yescomplemented
86#95×C59—24no—
87#95×C59—22no—
88#95×C59—42no—
89#95×C59D414yescomplemented
90C24×C59C2411yescharacteristic
91C23×D59—22no—
92C23×D59—22no—
93C23×D59—22no—
94C23×D59—22no—
95C23×D59—22no—
96C23×D59—22no—
97C23×D59—22no—
98C23×D59—22no—
99C23×D59—22no—
100C23×D59—22no—
101C23×D59—22no—
102C23×D59—22no—
103C23×D59C22×C414yes—
104C23×D59C2×D414yes—
105C23×D59C2×Q814yes—
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—21no—
115C22×C4×C59—22no—
116C22×C4×C59—22no—
117C22×C4×C59—22no—
118C22×C4×C59—22no—
119C22×C4×C59—21no—
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×C59C22×C412yes—
128C22×C4×C59C22×C412yes—
129C22×C4×C59C22×C412yes—
130C22×C4×C59C2×D414yes—
131C22×C4×C59C2×D412yes—
132C22×C4×C59C2×D412yes—
133C22×C4×C59C2×Q812yes—
134C22×C4×C59#4112yes—
135C22×Dic59—22no—
136C22×Dic59—22no—
137C22×Dic59—22no—
138C22×Dic59—22no—
139C22×Dic59—22no—
140C22×Dic59—22no—
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×Dic59C22×C414yes—
155C22×Dic59#4114yes—
156C2×D236—44no—
157C2×D236—44no—
158C2×D236—48no—
159C2×D236—48no—
160C2×D236C4⋊C4116yescomplemented
161C2×C4×D59—48no—
162C2×C4×D59—48no—
163C2×C4×D59—48no—
164C2×C4×D59—48no—
165C2×C4×D59—48no—
166C2×C4×D59—48no—
167C2×C4×D59—48no—
168C42×C59—44no—
169(C2×D59)⋊C4—216no—
170(C2×D59)⋊C4—48no—
171(C2×D59)⋊C4—48no—
172(C2×D59)⋊C4—48no—
173(C2×D59)⋊C4—48no—
174C4⋊Dic59—44no—
175C4⋊Dic59—48no—
176Dic59⋊C4—48no—
177C23×C59C23×C411yescharacteristic
178C23×C59C22×D411yescharacteristic
179C23×C59C22×D411yescharacteristic
180C23×C59C22×Q811yescharacteristic
181C23×C59C2×#4112yes—
182C23×C59C2×#4111yescharacteristic
183C23×C59H(5,𝔽2)12yes—
184C23×C59H(5,𝔽2)12yes—
185C23×C59H(5,𝔽2)12yes—
186C23×C59H(5,𝔽2)11yescharacteristic
187C23×C592−1+411yescharacteristic
188C22×D59—24no—
189C22×D59—24no—
190C22×D59—24no—
191C22×D59—24no—
192C22×D59—24no—
193C22×D59—24no—
194C22×D59—24no—
195C22×D59—24no—
196C22×D59—24no—
197C22×D59—24no—
198C22×D59—24no—
199C22×D59—24no—
200C22×D59—24no—
201C22×D59—24no—
202C22×D59—24no—
203C22×D59—24no—
204C22×D59—24no—
205C22×D59—24no—
206C22×D59—42no—
207C22×D59—42no—
208C22×D59—42no—
209C22×D59—42no—
210C22×D59—42no—
211C22×D59—42no—
212C22×D59—42no—
213C22×D59—42no—
214C22×D59—42no—
215C22×D59—42no—
216C22×D59—42no—
217C22×D59—42no—
218C22×D59—42no—
219C22×D59—42no—
220C22×D59—42no—
221C22×D59—42no—
222C22×D59C2×C4⋊C418yes—
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—22no—
232C2×C4×C59—22no—
233C2×C4×C59—22no—
234C2×C4×C59—24no—
235C2×C4×C59—24no—
236C2×C4×C59—24no—
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×C59—42no—
247C2×C4×C59—42no—
248C2×C4×C59—42no—
249C2×C4×C59—42no—
250C2×C4×C59C2×C4⋊C414yes—
251C2×C4×C59C4×D414yes—
252C2×Dic59—24no—
253C2×Dic59—24no—
254C2×Dic59—24no—
255C2×Dic59—24no—
256C2×Dic59—24no—
257C2×Dic59—24no—
258C2×Dic59—42no—
259C2×Dic59—42no—
260C2×Dic59—42no—
261C2×Dic59—42no—
262C2×Dic59—42no—
263C2×Dic59—42no—
264C2×Dic59—42no—
265C2×Dic59—42no—
266C2×Dic59—42no—
267C2×Dic59—42no—
268C2×Dic59—42no—
269C2×Dic59—42no—
270C2×Dic59—42no—
271C2×Dic59—42no—
272C2×Dic59—42no—
273D236—416no—
274C4×D59—432no—
275#14438—591nomaximal, Sylow
276C22×C59C22×C4⋊C411yescharacteristic
277C22×C59C2×C4×D411yescharacteristic
278C22×C59C4×#4111yescharacteristic
279C22×C59#51811yescharacteristic
280C22×C59#51811yescharacteristic
281C22×C59#51811yescharacteristic
282C22×C59#52011yescharacteristic
283C22×C59#53412yes—
284C22×C59#53512yes—
285C22×C59#53812yes—
286C22×C59#54012yes—
287C22×C59#54212yes—
288C22×C59#54312yes—
289C22×C59D4211yescharacteristic
290C22×C59#54612yes—
291C22×C59#54612yes—
292C22×C59#54711yescharacteristic
293C22×C59D4×Q811yescharacteristic
294C22×C59#55312yes—
295C22×C59#55412yes—
296C22×C59#55411yescharacteristic
297C22×C59#56012yes—
298C22×C59#56212yes—
299C2×D59—28no—
300C2×D59—28no—
301C2×D59—28no—
302C2×D59—44no—
303C2×D59—44no—
304C2×D59—44no—
305C2×D59—44no—
306C2×D59—44no—
307C2×D59—44no—
308C2×D59—44no—
309C2×D59—44no—
310C2×D59—44no—
311C2×D59—44no—
312C2×D59—44no—
313C2×D59—44no—
314C4×C59—24no—
315C4×C59—24no—
316C4×C59—42no—
317C4×C59—44no—
318C4×C59—82no—
319Dic59—44no—
320Dic59—44no—
321Dic59—82no—
322C2×#390—591no—
323C2×#386—592no—
324C2×#385—592no—
325#1441—592no—
326#1439—592no—
327#1439—592no—
328C4⋊#95—591no—
329#1434D5911yescharacteristic, complemented
330C22⋊#95—592no—
331C2×C59#231511yescharacteristic
332C2×C59#232811yescharacteristic
333C2×C59#233711yescharacteristic
334C2×C59D4×C4⋊C411yescharacteristic
335C2×C59#234911yescharacteristic
336C2×C59#236411yescharacteristic
337C2×C59#237711yescharacteristic
338C2×C59#267812yes—
339C2×C59#269212yes—
340C2×C59#270112yes—
341C2×C59#278012yes—
342D59—48no—
343C23×D4—591no—
344C24×C4—592no—
345C22×C4⋊C4—591no—
346C22×C4⋊C4—592no—
347C22×C4⋊C4—592no—
348C22×C22⋊C4—592no—
349C22×C22⋊C4—592no—
350C22×C22⋊C4—592no—
351C22×C22⋊C4—592no—
352C22×C22⋊C4—592no—
353C22×C42C2×D5911yescharacteristic
354#390—598no—
355#386—1188no—
356#385—1188no—
357C2×#95—592no—
358C2×#95—592no—
359C2×#95—591no—
360C2×#95—592no—
361C2×#95—591no—
362C2×#95—592no—
363C2×#95C2×D5911yescharacteristic
364C2×#95C2×D5912yes—
365C2×#95C2×D5912yes—
366C2×#95C2×D5911yescharacteristic
367C59#1443811yescharacteristic, complemented, Sylow
368C25—592no—
369C22×D4—594no—
370C22×D4—594no—
371C22×D4—594no—
372C22×D4—2362no—
373C22×D4—2362no—
374C23×C4—592no—
375C23×C4—592no—
376C23×C4—592no—
377C23×C4—1184no—
378C23×C4—1184no—
379C23×C4—1184no—
380C23×C4—2362no—
381C23×C4—2362no—
382C23×C4—2362no—
383C23×C4—2362no—
384C23×C4C22×D5912yes—
385C23×C4C22×D5911yescharacteristic
386C23×C4C22×D5912yes—
387C23×C4C22×D5911yescharacteristic
388C23×C4C22×D5911yescharacteristic
389C2×C4⋊C4—594no—
390C2×C4⋊C4—1184no—
391C2×C4⋊C4—1184no—
392C2×C4⋊C4—1184no—
393C2×C4⋊C4—2362no—
394C2×C4⋊C4—2362no—
395C2×C4⋊C4—2362no—
396C2×C4⋊C4—2362no—
397C2×C22⋊C4—598no—
398C2×C22⋊C4—598no—
399C2×C22⋊C4—1184no—
400C2×C22⋊C4—1184no—
401C2×C22⋊C4—1184no—
402C2×C22⋊C4—1184no—
403C2×C22⋊C4—1184no—
404C2×C22⋊C4—1184no—
405C2×C22⋊C4—1184no—
406C2×C22⋊C4—2362no—
407C2×C22⋊C4—2362no—
408C2×C22⋊C4—2362no—
409C2×C22⋊C4—2362no—
410C2×C22⋊C4—2362no—
411C2×C22⋊C4—2362no—
412C2×C42—42no—
413C2×C42C4×D5914yescomplemented
414#95—22no—
415#95—24no—
416#95—42no—
417#95—1184no—
418#95—1184no—
419#95—2361no—
420#95—2361no—
421#95—2362no—
422#95—2362no—
423#95D23614yescomplemented
424C24—594no—
425C24—594no—
426C24—594no—
427C24—1182no—
428C24—1182no—
429C24—1182no—
430C24—1182no—
431C24—1182no—
432C24—1182no—
433C24—1182no—
434C24—1182no—
435C24—1182no—
436C24—1182no—
437C24—1182no—
438C24—1182no—
439C24C23×D5911yescharacteristic
440C2×D4—5916no—
441C2×D4—2368no—
442C2×D4—2368no—
443C2×D4—2364no—
444C2×D4—2364no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—594no—
467C22×C4—594no—
468C22×C4—1182no—
469C22×C4—1182no—
470C22×C4—1182no—
471C22×C4—1182no—
472C22×C4—1182no—
473C22×C4—1182no—
474C22×C4—1182no—
475C22×C4—1182no—
476C22×C4—1182no—
477C22×C4—1182no—
478C22×C4—1182no—
479C22×C4—1182no—
480C22×C4—1182no—
481C22×C4—1182no—
482C22×C4—1182no—
483C22×C4—1182no—
484C22×C4—1182no—
485C22×C4—1182no—
486C22×C4—1182no—
487C22×C4—2368no—
488C22×C4—2368no—
489C22×C4—2368no—
490C22×C4—2368no—
491C22×C4—2368no—
492C22×C4—2368no—
493C22×C4—2368no—
494C22×C4C2×C4×D5912yes—
495C22×C4C2×C4×D5912yes—
496C22×C4C2×C4×D5912yes—
497C22×C4C2×D23614yes—
498C22×C4C2×D23612yes—
499C22×C4#1174568512yes—
500C22×C4D4×D5912yes—
501C22×C4Q8×D5912yes—
502C4⋊C4—2364no—
503C4⋊C4—2368no—
504C4⋊C4—2368no—
505C22⋊C4—11816no—
506C22⋊C4—2368no—
507C22⋊C4—2368no—
508C22⋊C4—2368no—
509C22⋊C4—2368no—
510C42—44no—
511C23—598no—
512C23—1184no—
513C23—1184no—
514C23—1184no—
515C23—1184no—
516C23—1184no—
517C23—1184no—
518C23—1184no—
519C23—1184no—
520C23—1184no—
521C23—1184no—
522C23—1184no—
523C23—1184no—
524C23—1184no—
525C23—1184no—
526C23—1184no—
527C23—1184no—
528C23—1184no—
529C23—1184no—
530C23—2362no—
531C23—2362no—
532C23—2362no—
533C23—2362no—
534C23—2362no—
535C23—2362no—
536C23—2362no—
537C23—2362no—
538C23—2362no—
539C23—2362no—
540C23—2362no—
541C23—2362no—
542C23—2362no—
543C23—2362no—
544C23—2362no—
545C23—2362no—
546C23C22×C4×D5911yescharacteristic
547C23C2×D4×D5911yescharacteristic
548C23C22×D23611yescharacteristic
549C23C2×Q8×D5911yescharacteristic
550C23#41×D5912yes—
551C23C2×#1174568511yescharacteristic
552C23#1427377212yes—
553C23#1427377312yes—
554C23#1427377312yes—
555C23#1427377311yescharacteristic
556C23#1427377411yescharacteristic
557D4—23616no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
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—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—1184no—
586C2×C4—1184no—
587C2×C4—1184no—
588C2×C4—1184no—
589C2×C4—1184no—
590C2×C4—1184no—
591C2×C4—23632no—
592C2×C4—2362no—
593C2×C4—2362no—
594C2×C4—2362no—
595C2×C4—2362no—
596C2×C4—2362no—
597C2×C4—2362no—
598C2×C4—2362no—
599C2×C4—2362no—
600C2×C4—2362no—
601C2×C4—2362no—
602C2×C4—2362no—
603C2×C4—2362no—
604C2×C4—2362no—
605C2×C4—2362no—
606C2×C4—2362no—
607C2×C4C4⋊C4×D5914yes—
608C2×C4C4×D23614yes—
609C22—1188no—
610C22—1188no—
611C22—1188no—
612C22—2364no—
613C22—2364no—
614C22—2364no—
615C22—2364no—
616C22—2364no—
617C22—2364no—
618C22—2364no—
619C22—2364no—
620C22—2364no—
621C22—2364no—
622C22—2364no—
623C22—2364no—
624C22C2×C4⋊C4×D5911yescharacteristic
625C22C2×C4×D23611yescharacteristic
626C22#1683787011yescharacteristic
627C22#1683787511yescharacteristic
628C22#1683787611yescharacteristic
629C22#1683787611yescharacteristic
630C22#1683788211yescharacteristic
631C22#1683796012yes—
632C22#1683797112yes—
633C22#1683799112yes—
634C22#1683800712yes—
635C22#1683801812yes—
636C22#1683802712yes—
637C22D4×D23611yescharacteristic
638C22#1683804512yes—
639C22#1683804712yes—
640C22#1683805711yescharacteristic
641C22Q8×D23611yescharacteristic
642C22#1683810112yes—
643C22#1683810812yes—
644C22#1683811211yescharacteristic
645C22#1683814212yes—
646C22#1683814912yes—
647C4—24no—
648C4—24no—
649C4—42no—
650C4—44no—
651C4—82no—
652C4—4722no—
653C4—2364no—
654C4—2364no—
655C2—2368no—
656C2#2142670911yescharacteristic
657C2#2142682111yescharacteristic
658C2#2142690611yescharacteristic
659C2C4⋊C4×D23611yescharacteristic
660C2#2142700411yescharacteristic
661C2#2142714611yescharacteristic
662C2#2142725511yescharacteristic
663C2#2143041912yes—
664C2#2143059012yes—
665C2#2143070612yes—
666C2#2143174712yes—
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×#1434C2
socle, cosocleC24×C59C24
prime radicalC23×D236C22
hypercenter#1434D59
hypocenterC59#14438
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#16837276C2semidirect
4. #21422348C2semidirect
5. #21422342C2semidirect
6. #21422340C2semidirect
7. #21422326C2semidirect
8. (C2×D59)⋊#95C2semidirect
9. C59×#1434C2semidirect
20. #16837304C4semidirect
54. C2×C4⋊Dic59C2×C4semidirect
71. C2×(C2×D59)⋊C4C2×C4semidirect
72. C2×(C2×D59)⋊C4C2×C4semidirect
85. C2×C42×C59C2×C4semidirect
89. #95×C59D4semidirect
160. C2×D236C4⋊C4semidirect
329. #1434D59semidirect
367. C59#14438semidirect
413. C2×C42C4×D59semidirect
423. #95D236semidirect

Maximal subgroups

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

subgroupindex
C2×#168373042
C2×#168372802
C2×#168372762
#214223482
#214223422
#214223402
#214223262
(C2×D59)⋊#952
C59×#14342
#1443859