Finite Group Databasebeta

← #28512409

Subgroups — #28512409

Order 15104.

1530 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837301C211yesmaximal, characteristic
2C2×#16837301C211yesmaximal, characteristic
3C2×#16837300C211yesmaximal, characteristic
4C2×C4×Dic59⋊C4C211yesmaximal, characteristic
5#21422360C212yesmaximal
6#21422348C212yesmaximal
7#21422329C212yesmaximal
8#21422326C212yesmaximal
9#21422325C211yesmaximal, characteristic
10#21422325C211yesmaximal, characteristic
11C2×C4×C4⋊C4×C59C211yesmaximal, characteristic
12C22×C4⋊Dic59C2211yescharacteristic
13C22×C4⋊Dic59C2212yes—
14C22×C4⋊Dic59C2211yescharacteristic
15C22×C4⋊Dic59C2212yes—
16C22×Dic59⋊C4C2211yescharacteristic
17C22×Dic59⋊C4C2211yescharacteristic
18C22×Dic59⋊C4C2212yes—
19C22×C4×Dic59C2211yescharacteristic
20C22×C4×Dic59C2211yescharacteristic
21#16837301—24no—
22#16837301C418yescomplemented
23#16837300—24no—
24C4×Dic59⋊C4—24no—
25C2×C59⋊#95C2211yescharacteristic
26C2×C59⋊#95C2211yescharacteristic
27C2×C59⋊#95C2212yes—
28C2×C59⋊#95C2212yes—
29C2×C59⋊#95C2212yes—
30C2×C59⋊#95C2212yes—
31C2×C59⋊#95C2212yes—
32C2×C59⋊#95C2212yes—
33C2×C59⋊#95C2212yes—
34C22×C4⋊C4×C59C2211yescharacteristic
35C22×C4⋊C4×C59C2211yescharacteristic
36C22×C42×C59C2212yes—
37C22×C42×C59C2211yescharacteristic
38C4×C4⋊C4×C59—24no—
39C2×#95×C59C2212yes—
40C23×Dic59C2312yes—
41C23×Dic59C2311yescharacteristic
42C23×Dic59C2312yes—
43C23×Dic59C2311yescharacteristic
44C23×Dic59C2311yescharacteristic
45C23×Dic59C2311yescharacteristic
46C2×C4⋊Dic59—22no—
47C2×C4⋊Dic59—22no—
48C2×C4⋊Dic59—22no—
49C2×C4⋊Dic59—24no—
50C2×C4⋊Dic59—22no—
51C2×C4⋊Dic59—22no—
52C2×C4⋊Dic59—24no—
53C2×C4⋊Dic59—42no—
54C2×C4⋊Dic59—42no—
55C2×C4⋊Dic59—42no—
56C2×C4⋊Dic59C2×C414yes—
57C2×C4⋊Dic59C2×C418yes—
58C2×Dic59⋊C4—22no—
59C2×Dic59⋊C4—22no—
60C2×Dic59⋊C4—22no—
61C2×Dic59⋊C4—22no—
62C2×Dic59⋊C4—22no—
63C2×Dic59⋊C4—24no—
64C2×Dic59⋊C4—42no—
65C2×Dic59⋊C4—42no—
66C2×Dic59⋊C4Q814yes—
67C2×C4×Dic59—22no—
68C2×C4×Dic59—22no—
69C2×C4×Dic59—22no—
70C2×C4×Dic59—22no—
71C2×C4×Dic59—22no—
72C2×C4×Dic59C2×C414yes—
73C59⋊#95—22no—
74C59⋊#95—22no—
75C59⋊#95—24no—
76C59⋊#95—24no—
77C59⋊#95—24no—
78C59⋊#95—42no—
79C59⋊#95—42no—
80C59⋊#95—42no—
81C59⋊#95C2×C418yes—
82C23×C4×C59C2311yescharacteristic
83C23×C4×C59C2312yes—
84C23×C4×C59C2312yes—
85C23×C4×C59C2311yescharacteristic
86C23×C4×C59C2311yescharacteristic
87C2×C4⋊C4×C59—22no—
88C2×C4⋊C4×C59—22no—
89C2×C4⋊C4×C59C2×C414yes—
90C2×C4⋊C4×C59D414yes—
91C2×C4⋊C4×C59Q814yes—
92C2×C4⋊C4×C59Q814yes—
93C2×C42×C59—22no—
94C2×C42×C59—22no—
95C2×C42×C59—24no—
96C2×C42×C59—24no—
97C2×C42×C59—42no—
98C2×C42×C59D414yes—
99#95×C59—24no—
100C24×C59C2411yescharacteristic
101C22×C4×C59—21no—
102C22×C4×C59—22no—
103C22×C4×C59—21no—
104C22×C4×C59—22no—
105C22×C4×C59—21no—
106C22×C4×C59—22no—
107C22×C4×C59—22no—
108C22×C4×C59—21no—
109C22×C4×C59—21no—
110C22×C4×C59—22no—
111C22×C4×C59—21no—
112C22×C4×C59—22no—
113C22×C4×C59—22no—
114C22×C4×C59—22no—
115C22×C4×C59—21no—
116C22×C4×C59—21no—
117C22×C4×C59—22no—
118C22×C4×C59—22no—
119C22×C4×C59—21no—
120C22×C4×C59—21no—
121C22×C4×C59C22×C414yes—
122C22×C4×C59C22×C412yes—
123C22×C4×C59C2×D412yes—
124C22×C4×C59C2×D414yes—
125C22×C4×C59C2×D412yes—
126C22×C4×C59C2×D412yes—
127C22×C4×C59C2×D412yes—
128C22×C4×C59C2×Q814yes—
129C22×C4×C59C2×Q814yes—
130C22×C4×C59C2×Q812yes—
131C22×C4×C59C2×Q812yes—
132C22×C4×C59C2×Q812yes—
133C22×C4×C59#4112yes—
134C22×C4×C59#4112yes—
135C22×C4×C59#4112yes—
136C22×Dic59—21no—
137C22×Dic59—21no—
138C22×Dic59—21no—
139C22×Dic59—21no—
140C22×Dic59—21no—
141C22×Dic59—21no—
142C22×Dic59—21no—
143C22×Dic59—21no—
144C22×Dic59—22no—
145C22×Dic59—21no—
146C22×Dic59—21no—
147C22×Dic59—21no—
148C22×Dic59—21no—
149C22×Dic59—21no—
150C22×Dic59—21no—
151C22×Dic59—22no—
152C22×Dic59—21no—
153C22×Dic59—21no—
154C22×Dic59—21no—
155C22×Dic59—22no—
156C22×Dic59—22no—
157C22×Dic59—22no—
158C22×Dic59—21no—
159C22×Dic59—21no—
160C22×Dic59—21no—
161C22×Dic59—21no—
162C22×Dic59—22no—
163C22×Dic59—21no—
164C22×Dic59—22no—
165C22×Dic59—22no—
166C22×Dic59—22no—
167C22×Dic59—22no—
168C22×Dic59—22no—
169C22×Dic59—22no—
170C22×Dic59—22no—
171C22×Dic59C22×C414yes—
172C22×Dic59C22×C412yes—
173C22×Dic59C22×C412yes—
174C22×Dic59C2×Q812yes—
175C22×Dic59C2×Q812yes—
176C22×Dic59#4112yes—
177C22×Dic59#4112yes—
178C4⋊C4×C59—28no—
179C4⋊C4×C59C4⋊C4116yescomplemented
180C42×C59—28no—
181C42×C59—48no—
182C4⋊Dic59—28no—
183C4⋊Dic59—48no—
184C4⋊Dic59—48no—
185C4⋊Dic59—44no—
186Dic59⋊C4—28no—
187Dic59⋊C4—28no—
188Dic59⋊C4—48no—
189C4×Dic59—28no—
190C4×Dic59—44no—
191C23×C59C23×C411yescharacteristic
192C23×C59C22×D411yescharacteristic
193C23×C59C22×D411yescharacteristic
194C23×C59C22×Q811yescharacteristic
195C23×C59C22×Q811yescharacteristic
196C23×C59C22×Q811yescharacteristic
197C23×C59C2×#4111yescharacteristic
198C23×C59C2×#4111yescharacteristic
199C23×C59C2×#4111yescharacteristic
200C23×C59C2×#4111yescharacteristic
201C23×C59C2×#4111yescharacteristic
202C23×C59H(5,𝔽2)11yescharacteristic
203C23×C59H(5,𝔽2)11yescharacteristic
204C23×C59H(5,𝔽2)11yescharacteristic
205C23×C592−1+411yescharacteristic
206C2×C4×C59—24no—
207C2×C4×C59—24no—
208C2×C4×C59—22no—
209C2×C4×C59—22no—
210C2×C4×C59—24no—
211C2×C4×C59—22no—
212C2×C4×C59—24no—
213C2×C4×C59—22no—
214C2×C4×C59—22no—
215C2×C4×C59—22no—
216C2×C4×C59—24no—
217C2×C4×C59—24no—
218C2×C4×C59—22no—
219C2×C4×C59—24no—
220C2×C4×C59—22no—
221C2×C4×C59—22no—
222C2×C4×C59—24no—
223C2×C4×C59—24no—
224C2×C4×C59—42no—
225C2×C4×C59—42no—
226C2×C4×C59—42no—
227C2×C4×C59—41no—
228C2×C4×C59—41no—
229C2×C4×C59—42no—
230C2×C4×C59—41no—
231C2×C4×C59—41no—
232C2×C4×C59C2×C4⋊C418yes—
233C2×C4×C59C2×C4⋊C414yes—
234C2×C4×C59C4×D414yes—
235C2×C4×C59C4×Q814yes—
236C2×C4×C59#12114yes—
237C2×C4×C59C22⋊Q814yes—
238C2×C4×C59C22⋊Q814yes—
239C2×C4×C59#12514yes—
240C2×C4×C59C4⋊Q814yes—
241C2×Dic59—22no—
242C2×Dic59—22no—
243C2×Dic59—22no—
244C2×Dic59—22no—
245C2×Dic59—22no—
246C2×Dic59—22no—
247C2×Dic59—22no—
248C2×Dic59—24no—
249C2×Dic59—22no—
250C2×Dic59—24no—
251C2×Dic59—22no—
252C2×Dic59—24no—
253C2×Dic59—22no—
254C2×Dic59—22no—
255C2×Dic59—22no—
256C2×Dic59—22no—
257C2×Dic59—22no—
258C2×Dic59—22no—
259C2×Dic59—41no—
260C2×Dic59—41no—
261C2×Dic59—42no—
262C2×Dic59—41no—
263C2×Dic59—41no—
264C2×Dic59—41no—
265C2×Dic59—42no—
266C2×Dic59—41no—
267C2×Dic59—41no—
268C2×Dic59—42no—
269C2×Dic59—41no—
270C2×Dic59—42no—
271C2×Dic59—41no—
272C2×Dic59—41no—
273C2×Dic59—41no—
274C2×Dic59—41no—
275C2×Dic59—42no—
276C2×Dic59—42no—
277C2×Dic59—42no—
278C2×Dic59—42no—
279C2×Dic59—42no—
280C2×Dic59—42no—
281C2×Dic59—42no—
282C2×Dic59C4×Q814yes—
283#14045—591nomaximal, Sylow
284C22×C59C22×C4⋊C411yescharacteristic
285C22×C59C2×C4×D411yescharacteristic
286C22×C59C2×C4×Q811yescharacteristic
287C22×C59C2×C4×Q811yescharacteristic
288C22×C59C4×#4111yescharacteristic
289C22×C59#51811yescharacteristic
290C22×C59#52011yescharacteristic
291C22×C59C2×#12111yescharacteristic
292C22×C59C2×C22⋊Q811yescharacteristic
293C22×C59C2×C22⋊Q811yescharacteristic
294C22×C59#52511yescharacteristic
295C22×C59C2×#12511yescharacteristic
296C22×C59#52911yescharacteristic
297C22×C59C2×C4⋊Q811yescharacteristic
298C22×C59#53311yescharacteristic
299C22×C59#53511yescharacteristic
300C22×C59#53711yescharacteristic
301C22×C59#54011yescharacteristic
302C22×C59#54211yescharacteristic
303C22×C59#54611yescharacteristic
304C22×C59#54611yescharacteristic
305C22×C59D4×Q811yescharacteristic
306C22×C59#55011yescharacteristic
307C22×C59#55211yescharacteristic
308C22×C59#55311yescharacteristic
309C22×C59#55411yescharacteristic
310C22×C59#55411yescharacteristic
311C22×C59#55411yescharacteristic
312C22×C59#55411yescharacteristic
313C22×C59#55411yescharacteristic
314C22×C59#55511yescharacteristic
315C22×C59#55711yescharacteristic
316C22×C59#55711yescharacteristic
317C22×C59Q8211yescharacteristic
318C22×C59Q8211yescharacteristic
319C4×C59—28no—
320C4×C59—24no—
321C4×C59—42no—
322C4×C59—44no—
323C4×C59#38918yes—
324Dic59—24no—
325Dic59—42no—
326Dic59—44no—
327Dic59—42no—
328Dic59—42no—
329Dic59—82no—
330C2×#389—591no—
331C2×#389—591no—
332C2×#389—591no—
333C2×C4×C4⋊C4—591no—
334C2×C4×C4⋊C4D5911yescharacteristic
335#1444—592no—
336#1441—592no—
337#1436—592no—
338C4⋊#95—592no—
339C4⋊#95—591no—
340C4⋊#95—591no—
341C2×C59C2×#38911yescharacteristic
342C2×C59C4×C22⋊Q811yescharacteristic
343C2×C59#232411yescharacteristic
344C2×C59#234911yescharacteristic
345C2×C59Q8×C4⋊C411yescharacteristic
346C2×C59#236911yescharacteristic
347C2×C59#237011yescharacteristic
348C2×C59#241411yescharacteristic
349C2×C59#241711yescharacteristic
350C2×C59#245111yescharacteristic
351C2×C59#245411yescharacteristic
352C2×C59#250711yescharacteristic
353C2×C59#250811yescharacteristic
354C2×C59#256711yescharacteristic
355C2×C59#258411yescharacteristic
356C22×C4⋊C4—591no—
357C22×C4⋊C4—591no—
358C22×C4⋊C4—592no—
359C22×C4⋊C4—591no—
360C22×C4⋊C4—591no—
361C22×C4⋊C4—592no—
362C22×C4⋊C4—592no—
363C22×C4⋊C4C2×D5911yescharacteristic
364C22×C4⋊C4C2×D5911yescharacteristic
365C22×C42—591no—
366C22×C42—591no—
367C22×C42C2×D5912yes—
368C22×C42C2×D5911yescharacteristic
369#389—598no—
370#389—1184no—
371#389—1184no—
372C4×C4⋊C4—24no—
373C4×C4⋊C4—1184no—
374C2×#95—592no—
375C2×#95—591no—
376C2×#95—592no—
377C2×#95—592no—
378C2×#95—592no—
379C2×#95—591no—
380C2×#95—592no—
381C2×#95—592no—
382C2×#95—592no—
383C2×#95C2×D5912yes—
384C59#1404511yescharacteristic, complemented, Sylow
385C23×C4—591no—
386C23×C4—592no—
387C23×C4—591no—
388C23×C4—591no—
389C23×C4—591no—
390C23×C4—592no—
391C23×C4C22×D5912yes—
392C23×C4C22×D5911yescharacteristic
393C23×C4C22×D5912yes—
394C23×C4C22×D5911yescharacteristic
395C23×C4C22×D5911yescharacteristic
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—594no—
399C2×C4⋊C4—594no—
400C2×C4⋊C4—598no—
401C2×C4⋊C4—1182no—
402C2×C4⋊C4—1182no—
403C2×C4⋊C4—1182no—
404C2×C4⋊C4—1182no—
405C2×C4⋊C4—1182no—
406C2×C4⋊C4—1182no—
407C2×C4⋊C4—1182no—
408C2×C4⋊C4—1184no—
409C2×C4⋊C4—1184no—
410C2×C4⋊C4—1182no—
411C2×C4⋊C4—1182no—
412C2×C4⋊C4—1184no—
413C2×C4⋊C4—1182no—
414C2×C4⋊C4—2362no—
415C2×C4⋊C4—2362no—
416C2×C4⋊C4—2362no—
417C2×C4⋊C4—2362no—
418C2×C4⋊C4—2362no—
419C2×C4⋊C4Dic11814yes—
420C2×C4⋊C4Dic11814yes—
421C2×C4⋊C4C4×D5914yes—
422C2×C4⋊C4C22⋊D5914yes—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—24no—
426C2×C42—24no—
427C2×C42—42no—
428C2×C42—594no—
429C2×C42—1182no—
430C2×C42—1182no—
431C2×C42—1182no—
432C2×C42—1182no—
433C2×C42—1182no—
434C2×C42D23614yes—
435#95—24no—
436#95—598no—
437#95—1184no—
438#95—1182no—
439#95—1182no—
440#95—1184no—
441#95—1184no—
442#95—2362no—
443#95—2362no—
444#95—2362no—
445C24C23×D5911yescharacteristic
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—592no—
467C22×C4—592no—
468C22×C4—592no—
469C22×C4—594no—
470C22×C4—592no—
471C22×C4—592no—
472C22×C4—592no—
473C22×C4—1181no—
474C22×C4—1181no—
475C22×C4—1181no—
476C22×C4—1181no—
477C22×C4—1181no—
478C22×C4—1181no—
479C22×C4—1181no—
480C22×C4—1181no—
481C22×C4—1181no—
482C22×C4—1182no—
483C22×C4—1181no—
484C22×C4—1181no—
485C22×C4—1181no—
486C22×C4—1181no—
487C22×C4—1181no—
488C22×C4—1182no—
489C22×C4—1181no—
490C22×C4—1182no—
491C22×C4—1181no—
492C22×C4—1181no—
493C22×C4—1181no—
494C22×C4—1182no—
495C22×C4—1181no—
496C22×C4—1181no—
497C22×C4—1182no—
498C22×C4—1181no—
499C22×C4—1182no—
500C22×C4—1181no—
501C22×C4—1182no—
502C22×C4—1182no—
503C22×C4—1182no—
504C22×C4—1182no—
505C22×C4—1182no—
506C22×C4—1182no—
507C22×C4—1182no—
508C22×C4C2×Dic11814yes—
509C22×C4C2×Dic11814yes—
510C22×C4C2×Dic11812yes—
511C22×C4C2×Dic11812yes—
512C22×C4C2×C4×D5914yes—
513C22×C4C2×C4×D5912yes—
514C22×C4C2×D23612yes—
515C22×C4C2×D23612yes—
516C22×C4C2×D23612yes—
517C22×C4#1174568512yes—
518C22×C4#1174568512yes—
519C22×C4#1174568712yes—
520C22×C4Q8×D5912yes—
521C22×C4C2×C22⋊D5914yes—
522C22×C4C2×C22⋊D5912yes—
523C4⋊C4—28no—
524C4⋊C4—1188no—
525C4⋊C4—1188no—
526C4⋊C4—1188no—
527C4⋊C4—2368no—
528C4⋊C4—2368no—
529C4⋊C4—2368no—
530C4⋊C4—2364no—
531C4⋊C4Dic59⋊C4116yescomplemented
532C42—28no—
533C42—48no—
534C42—1188no—
535C42—2364no—
536C23C22×C4×D5911yescharacteristic
537C23C22×C22⋊D5911yescharacteristic
538C23C22×D23611yescharacteristic
539C23C2×Q8×D5911yescharacteristic
540C23C22×Dic11811yescharacteristic
541C23C22×Dic11811yescharacteristic
542C23#41×D5911yescharacteristic
543C23#41×D5911yescharacteristic
544C23C2×#1174568711yescharacteristic
545C23C2×#1174568511yescharacteristic
546C23C2×#1174568511yescharacteristic
547C23#1427377211yescharacteristic
548C23#1427377311yescharacteristic
549C23#1427377311yescharacteristic
550C23#1427377511yescharacteristic
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—594no—
578C2×C4—1182no—
579C2×C4—1182no—
580C2×C4—1182no—
581C2×C4—1182no—
582C2×C4—1182no—
583C2×C4—1182no—
584C2×C4—1182no—
585C2×C4—1182no—
586C2×C4—1182no—
587C2×C4—1182no—
588C2×C4—1182no—
589C2×C4—1182no—
590C2×C4—1182no—
591C2×C4—1184no—
592C2×C4—1182no—
593C2×C4—1184no—
594C2×C4—1184no—
595C2×C4—1182no—
596C2×C4—2362no—
597C2×C4—2362no—
598C2×C4—2362no—
599C2×C4—2362no—
600C2×C4—2362no—
601C2×C4—2362no—
602C2×C4—2362no—
603C2×C4—2361no—
604C2×C4—2361no—
605C2×C4—2362no—
606C2×C4—2361no—
607C2×C4—2361no—
608C2×C4—2361no—
609C2×C4—2361no—
610C2×C4—2362no—
611C2×C4—2361no—
612C2×C4—2362no—
613C2×C4—2361no—
614C2×C4—2362no—
615C2×C4—2361no—
616C2×C4—2361no—
617C2×C4—2361no—
618C2×C4—2361no—
619C2×C4C2×Dic59⋊C418yes—
620C2×C4C2×Dic59⋊C414yes—
621C2×C4C4×D23614yes—
622C2×C4C4×Dic11814yes—
623C2×C4#1427370114yes—
624C2×C4#1427370614yes—
625C2×C4#1427370714yes—
626C2×C4#1427371914yes—
627C2×C4#1427372714yes—
628C22C22×Dic59⋊C411yescharacteristic
629C22C2×C4×D23611yescharacteristic
630C22C4×Q8×D5911yescharacteristic
631C22C2×C4×Dic11811yescharacteristic
632C22C4×#1174568711yescharacteristic
633C22#1683787411yescharacteristic
634C22#1683788411yescharacteristic
635C22C2×#1427370111yescharacteristic
636C22C2×#1427370611yescharacteristic
637C22C2×#1427370711yescharacteristic
638C22#1683791411yescharacteristic
639C22C2×#1427371911yescharacteristic
640C22#1683793411yescharacteristic
641C22C2×#1427372711yescharacteristic
642C22#1683795611yescharacteristic
643C22#1683797111yescharacteristic
644C22#1683798311yescharacteristic
645C22#1683800311yescharacteristic
646C22#1683802411yescharacteristic
647C22#1683804011yescharacteristic
648C22#1683804611yescharacteristic
649C22Q8×C22⋊D5911yescharacteristic
650C22#1683807111yescharacteristic
651C22#1683808711yescharacteristic
652C22#1683809611yescharacteristic
653C22#1683810711yescharacteristic
654C22#1683810911yescharacteristic
655C22#1683810911yescharacteristic
656C22#1683811111yescharacteristic
657C22#1683811111yescharacteristic
658C22#1683811511yescharacteristic
659C22#1683812811yescharacteristic
660C22#1683812811yescharacteristic
661C22Q8×Dic11811yescharacteristic
662C22Q8×Dic11811yescharacteristic
663C4—28no—
664C4—24no—
665C4—42no—
666C4—44no—
667C4—1184no—
668C4—4722no—
669C4—2362no—
670C4—2362no—
671C4—2362no—
672C4—2364no—
673C4#1683730018yes—
674C2C2×#1683730011yescharacteristic
675C2C4×#1427370711yescharacteristic
676C2#2142679011yescharacteristic
677C2#2142700111yescharacteristic
678C2Q8×Dic59⋊C411yescharacteristic
679C2#2142718311yescharacteristic
680C2#2142719411yescharacteristic
681C2#2142750811yescharacteristic
682C2#2142754111yescharacteristic
683C2#2142792911yescharacteristic
684C2#2142796211yescharacteristic
685C2#2142861711yescharacteristic
686C2#2142862811yescharacteristic
687C2#2142930411yescharacteristic
688C2#2142947911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C4×C4⋊C4×C59C2
socle, prime radical, cosocleC24×C59C24
hypercenterC2×C4×C4⋊C4D59
hypocenterC59#14045
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
22. #16837301C4semidirect
179. C4⋊C4×C59C4⋊C4semidirect
384. C59#14045semidirect
531. C4⋊C4Dic59⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#168373012
C2×#168373002
C2×C4×Dic59⋊C42
#214223602
#214223482
#214223292
#214223262
#214223252
C2×C4×C4⋊C4×C592
#1404559