Finite Group Databasebeta

← #28511773

Subgroups — #28511773

Order 15104.

1746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837298C211yesmaximal, characteristic, complemented
2C2×#16837259C211yesmaximal, characteristic
3C2×#16837259C211yesmaximal, characteristic
4C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic
5#21422356C212yesmaximal, complemented
6#21422340C212yesmaximal
7#21422334C212yesmaximal
8#21422329C212yesmaximal, complemented
9#21422326C211yesmaximal, characteristic, complemented
10#21422325C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊C4×C59C211yesmaximal, characteristic, complemented
12C23×C4×D59C2211yescharacteristic
13C22×C4⋊Dic59C2211yescharacteristic
14C22×C4⋊Dic59C2211yescharacteristic
15C22×Dic59⋊C4C2212yes—
16C22×(C2×D59)⋊C4C2211yescharacteristic
17C22×(C2×D59)⋊C4C2212yes—
18C22×(C2×D59)⋊C4C2211yescharacteristic
19C22×(C2×D59)⋊C4C2212yes—
20C22×C4×Dic59C2211yescharacteristic
21#16837298—24no—
22#16837259—24no—
23#16837259C418yescomplemented
24C4×(C2×D59)⋊C4—24no—
25C2×C59⋊#95C2211yescharacteristic
26C2×C59⋊#95C2212yes—
27C2×C59⋊#95C2212yes—
28C2×C59⋊#95C2212yes—
29C2×C59⋊#95C2211yescharacteristic
30C2×C59⋊#95C2212yes—
31C2×C59⋊#95C2212yes—
32C2×C59⋊#95C2212yes—
33C2×C59⋊#95C2212yes—
34C22×C4⋊C4×C59C2211yescharacteristic
35C22×C4⋊C4×C59C2211yescharacteristic
36C22×C42×C59C2211yescharacteristic
37C22×C42×C59C2212yes—
38C4×C4⋊C4×C59—24no—
39C2×#95×C59C2212yes—
40C24×D59C2311yescharacteristic
41C23×Dic59C2312yes—
42C23×Dic59C2311yescharacteristic
43C23×Dic59C2312yes—
44C23×Dic59C2311yescharacteristic
45C23×Dic59C2311yescharacteristic
46C22×C4×D59—22no—
47C22×C4×D59—22no—
48C22×C4×D59—22no—
49C22×C4×D59—22no—
50C22×C4×D59—22no—
51C22×C4×D59—22no—
52C22×C4×D59C2×C414yes—
53C2×C4⋊Dic59—22no—
54C2×C4⋊Dic59—22no—
55C2×C4⋊Dic59—22no—
56C2×C4⋊Dic59—22no—
57C2×C4⋊Dic59—22no—
58C2×C4⋊Dic59C2×C414yes—
59C2×Dic59⋊C4—24no—
60C2×Dic59⋊C4—24no—
61C2×Dic59⋊C4—42no—
62C2×(C2×D59)⋊C4—22no—
63C2×(C2×D59)⋊C4—22no—
64C2×(C2×D59)⋊C4—22no—
65C2×(C2×D59)⋊C4—22no—
66C2×(C2×D59)⋊C4—22no—
67C2×(C2×D59)⋊C4—24no—
68C2×(C2×D59)⋊C4—24no—
69C2×(C2×D59)⋊C4—42no—
70C2×(C2×D59)⋊C4—42no—
71C2×(C2×D59)⋊C4—42no—
72C2×(C2×D59)⋊C4C2×C418yes—
73C2×(C2×D59)⋊C4Q814yes—
74C2×C4×Dic59—22no—
75C2×C4×Dic59—22no—
76C2×C4×Dic59—22no—
77C59⋊#95—22no—
78C59⋊#95—22no—
79C59⋊#95—24no—
80C59⋊#95—24no—
81C59⋊#95—24no—
82C59⋊#95—42no—
83C59⋊#95—42no—
84C59⋊#95—42no—
85C59⋊#95C2×C418yes—
86C23×C4×C59C2312yes—
87C23×C4×C59C2311yescharacteristic
88C23×C4×C59C2312yes—
89C23×C4×C59C2311yescharacteristic
90C23×C4×C59C2311yescharacteristic
91C2×C4⋊C4×C59—22no—
92C2×C4⋊C4×C59—22no—
93C2×C4⋊C4×C59—22no—
94C2×C4⋊C4×C59—22no—
95C2×C4⋊C4×C59C2×C414yes—
96C2×C4⋊C4×C59D414yes—
97C2×C42×C59—22no—
98C2×C42×C59—22no—
99C2×C42×C59—24no—
100C2×C42×C59—42no—
101C2×C42×C59—42no—
102C2×C42×C59D414yes—
103#95×C59—24no—
104C24×C59C2411yescharacteristic
105C23×D59—21no—
106C23×D59—21no—
107C23×D59—21no—
108C23×D59—21no—
109C23×D59—21no—
110C23×D59—21no—
111C23×D59—21no—
112C23×D59—21no—
113C23×D59—21no—
114C23×D59—21no—
115C23×D59—21no—
116C23×D59—21no—
117C23×D59C22×C412yes—
118C23×D59C2×Q812yes—
119C23×D59#4112yes—
120C22×C4×C59—21no—
121C22×C4×C59—21no—
122C22×C4×C59—21no—
123C22×C4×C59—21no—
124C22×C4×C59—22no—
125C22×C4×C59—22no—
126C22×C4×C59—21no—
127C22×C4×C59—21no—
128C22×C4×C59—22no—
129C22×C4×C59—22no—
130C22×C4×C59—21no—
131C22×C4×C59—21no—
132C22×C4×C59—22no—
133C22×C4×C59—22no—
134C22×C4×C59—22no—
135C22×C4×C59—22no—
136C22×C4×C59—22no—
137C22×C4×C59—22no—
138C22×C4×C59—21no—
139C22×C4×C59—22no—
140C22×C4×C59—22no—
141C22×C4×C59—21no—
142C22×C4×C59C22×C414yes—
143C22×C4×C59C22×C412yes—
144C22×C4×C59C2×D414yes—
145C22×C4×C59C2×D412yes—
146C22×C4×C59C2×D412yes—
147C22×C4×C59C2×D412yes—
148C22×C4×C59C2×D412yes—
149C22×C4×C59C2×Q812yes—
150C22×C4×C59#4112yes—
151C22×C4×C59#4112yes—
152C22×C4×C59#4112yes—
153C22×C4×C59#4112yes—
154C22×C4×C59#4112yes—
155C22×Dic59—21no—
156C22×Dic59—21no—
157C22×Dic59—21no—
158C22×Dic59—21no—
159C22×Dic59—21no—
160C22×Dic59—22no—
161C22×Dic59—21no—
162C22×Dic59—22no—
163C22×Dic59—21no—
164C22×Dic59—21no—
165C22×Dic59—21no—
166C22×Dic59—21no—
167C22×Dic59—22no—
168C22×Dic59—22no—
169C22×Dic59—21no—
170C22×Dic59—21no—
171C22×Dic59—21no—
172C22×Dic59—21no—
173C22×Dic59—21no—
174C22×Dic59—21no—
175C22×Dic59—22no—
176C22×Dic59—22no—
177C22×Dic59—21no—
178C22×Dic59—21no—
179C22×Dic59—22no—
180C22×Dic59—22no—
181C22×Dic59—22no—
182C22×Dic59—22no—
183C22×Dic59—22no—
184C22×Dic59—22no—
185C22×Dic59—22no—
186C22×Dic59C22×C412yes—
187C22×Dic59C22×C414yes—
188C22×Dic59C2×Q812yes—
189C22×Dic59#4112yes—
190C2×C4×D59—28no—
191C2×C4×D59—28no—
192C2×C4×D59—28no—
193C2×C4×D59—44no—
194C2×C4×D59—44no—
195C2×C4×D59—44no—
196C2×C4×D59—44no—
197C4⋊C4×C59—28no—
198C4⋊C4×C59—28no—
199C42×C59—28no—
200C42×C59—48no—
201(C2×D59)⋊C4—28no—
202(C2×D59)⋊C4—28no—
203(C2×D59)⋊C4—48no—
204(C2×D59)⋊C4—48no—
205C4⋊Dic59—28no—
206C4⋊Dic59—44no—
207Dic59⋊C4—48no—
208C4×Dic59—44no—
209C23×C59C23×C411yescharacteristic
210C23×C59C22×D411yescharacteristic
211C23×C59C22×D411yescharacteristic
212C23×C59C22×Q811yescharacteristic
213C23×C59C2×#4111yescharacteristic
214C23×C59C2×#4111yescharacteristic
215C23×C59C2×#4111yescharacteristic
216C23×C59C2×#4111yescharacteristic
217C23×C59C2×#4111yescharacteristic
218C23×C59C2×#4111yescharacteristic
219C23×C59C2×#4111yescharacteristic
220C23×C59H(5,𝔽2)11yescharacteristic
221C23×C59H(5,𝔽2)11yescharacteristic
222C23×C59H(5,𝔽2)11yescharacteristic
223C23×C592−1+411yescharacteristic
224C22×D59—22no—
225C22×D59—22no—
226C22×D59—22no—
227C22×D59—22no—
228C22×D59—22no—
229C22×D59—22no—
230C22×D59—22no—
231C22×D59—22no—
232C22×D59—22no—
233C22×D59—22no—
234C22×D59—22no—
235C22×D59—22no—
236C22×D59—22no—
237C22×D59—22no—
238C22×D59—22no—
239C22×D59—22no—
240C22×D59—22no—
241C22×D59—22no—
242C22×D59—41no—
243C22×D59—41no—
244C22×D59—41no—
245C22×D59—41no—
246C22×D59—41no—
247C22×D59—41no—
248C22×D59—41no—
249C22×D59—41no—
250C22×D59—41no—
251C22×D59—41no—
252C22×D59—41no—
253C22×D59—41no—
254C22×D59—41no—
255C22×D59—41no—
256C22×D59—41no—
257C22×D59—41no—
258C22×D59C4×Q814yes—
259C2×C4×C59—22no—
260C2×C4×C59—22no—
261C2×C4×C59—22no—
262C2×C4×C59—22no—
263C2×C4×C59—22no—
264C2×C4×C59—22no—
265C2×C4×C59—24no—
266C2×C4×C59—24no—
267C2×C4×C59—24no—
268C2×C4×C59—24no—
269C2×C4×C59—22no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—24no—
273C2×C4×C59—24no—
274C2×C4×C59—42no—
275C2×C4×C59—42no—
276C2×C4×C59—42no—
277C2×C4×C59—42no—
278C2×C4×C59—42no—
279C2×C4×C59—42no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—42no—
283C2×C4×C59—42no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59#11714yes—
287C2×C4×C59C4×D414yes—
288C2×C4×C59C4×D414yes—
289C2×C4×C59#12114yes—
290C2×C4×C59C22⋊Q814yes—
291C2×C4×C59#12314yes—
292C2×C4×C59#12414yes—
293C2×C4×C59#12614yes—
294C2×Dic59—22no—
295C2×Dic59—24no—
296C2×Dic59—22no—
297C2×Dic59—22no—
298C2×Dic59—24no—
299C2×Dic59—24no—
300C2×Dic59—22no—
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—41no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310C2×Dic59—41no—
311C2×Dic59—41no—
312C2×Dic59—41no—
313C2×Dic59—41no—
314C2×Dic59—42no—
315C2×Dic59—41no—
316C2×Dic59—42no—
317C2×Dic59—41no—
318C2×Dic59—42no—
319C2×Dic59—41no—
320C2×Dic59—42no—
321C2×Dic59—41no—
322C2×Dic59—42no—
323C2×Dic59—42no—
324C2×Dic59—42no—
325C2×Dic59—42no—
326C2×Dic59—42no—
327C2×Dic59—42no—
328C2×Dic59—42no—
329C4×D59—416no—
330#13993—591nomaximal, Sylow
331C22×C59C2×#11711yescharacteristic
332C22×C59C2×C4×D411yescharacteristic
333C22×C59C2×C4×D411yescharacteristic
334C22×C59C2×C4×Q811yescharacteristic
335C22×C59C4×#4111yescharacteristic
336C22×C59#51811yescharacteristic
337C22×C59#52011yescharacteristic
338C22×C59C2×#12111yescharacteristic
339C22×C59C2×C22⋊Q811yescharacteristic
340C22×C59C2×#12311yescharacteristic
341C22×C59#52511yescharacteristic
342C22×C59C2×#12411yescharacteristic
343C22×C59C2×#12611yescharacteristic
344C22×C59#52911yescharacteristic
345C22×C59#53311yescharacteristic
346C22×C59#53511yescharacteristic
347C22×C59#53711yescharacteristic
348C22×C59#54011yescharacteristic
349C22×C59#54211yescharacteristic
350C22×C59#54611yescharacteristic
351C22×C59#54611yescharacteristic
352C22×C59D4×Q811yescharacteristic
353C22×C59#55011yescharacteristic
354C22×C59#55211yescharacteristic
355C22×C59#55311yescharacteristic
356C22×C59#55311yescharacteristic
357C22×C59#55311yescharacteristic
358C22×C59#55311yescharacteristic
359C22×C59#55311yescharacteristic
360C22×C59#55411yescharacteristic
361C22×C59#55411yescharacteristic
362C22×C59#55411yescharacteristic
363C22×C59#55511yescharacteristic
364C22×C59#55611yescharacteristic
365C22×C59#55611yescharacteristic
366C2×D59—24no—
367C2×D59—24no—
368C2×D59—24no—
369C2×D59—42no—
370C2×D59—42no—
371C2×D59—42no—
372C2×D59—42no—
373C2×D59—42no—
374C2×D59—42no—
375C2×D59—42no—
376C2×D59—42no—
377C2×D59—42no—
378C2×D59—42no—
379C2×D59—42no—
380C2×D59—42no—
381C4×C59—24no—
382C4×C59—44no—
383C4×C59—42no—
384C4×C59—44no—
385C4×C59#38818yes—
386Dic59—44no—
387Dic59—42no—
388Dic59—42no—
389Dic59—42no—
390Dic59—82no—
391C2×#389—591no—
392C2×#380—591no—
393C2×#380—591no—
394C2×C4×C4⋊C4D5911yescharacteristic, complemented
395C2×C4×C22⋊C4—591no—
396#1443—592no—
397#1439—592no—
398#1437—592no—
399#1436—592no—
400C4⋊#95—591no—
401C4⋊#95—591no—
402C2×C59C2×#38811yescharacteristic
403C2×C59C4×C22⋊Q811yescharacteristic
404C2×C59#232411yescharacteristic
405C2×C59#234511yescharacteristic
406C2×C59#234711yescharacteristic
407C2×C59#236011yescharacteristic
408C2×C59#236311yescharacteristic
409C2×C59#248511yescharacteristic
410C2×C59#248711yescharacteristic
411C2×C59#249011yescharacteristic
412C2×C59#249211yescharacteristic
413C2×C59#249411yescharacteristic
414C2×C59#249711yescharacteristic
415C2×C59#253511yescharacteristic
416C2×C59#253811yescharacteristic
417D59—44no—
418C24×C4—591no—
419C22×C4⋊C4—591no—
420C22×C4⋊C4—591no—
421C22×C4⋊C4—592no—
422C22×C4⋊C4C2×D5911yescharacteristic
423C22×C4⋊C4C2×D5911yescharacteristic
424C22×C22⋊C4—591no—
425C22×C22⋊C4—592no—
426C22×C22⋊C4—591no—
427C22×C22⋊C4—592no—
428C22×C42—591no—
429C22×C42C2×D5911yescharacteristic
430C22×C42C2×D5912yes—
431#389—1184no—
432#380—598no—
433#380—1184no—
434C4×C4⋊C4—24no—
435C4×C22⋊C4—1184no—
436C2×#95—592no—
437C2×#95—592no—
438C2×#95—591no—
439C2×#95—592no—
440C2×#95—592no—
441C2×#95—591no—
442C2×#95—592no—
443C2×#95—592no—
444C2×#95—592no—
445C2×#95C2×D5912yes—
446C59#1399311yescharacteristic, complemented, Sylow
447C25—591no—
448C23×C4—592no—
449C23×C4—591no—
450C23×C4—591no—
451C23×C4—591no—
452C23×C4—594no—
453C23×C4—592no—
454C23×C4—1182no—
455C23×C4—1182no—
456C23×C4—1182no—
457C23×C4—1182no—
458C23×C4—1182no—
459C23×C4—1182no—
460C23×C4C22×D5912yes—
461C23×C4C22×D5912yes—
462C23×C4C22×D5911yescharacteristic
463C23×C4C22×D5911yescharacteristic
464C23×C4C22×D5911yescharacteristic
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—594no—
470C2×C4⋊C4—1182no—
471C2×C4⋊C4—1182no—
472C2×C4⋊C4—1184no—
473C2×C4⋊C4—1182no—
474C2×C4⋊C4—1184no—
475C2×C4⋊C4—1182no—
476C2×C4⋊C4—1182no—
477C2×C4⋊C4—2362no—
478C2×C4⋊C4C4×D5914yes—
479C2×C4⋊C4D23614yes—
480C2×C22⋊C4—594no—
481C2×C22⋊C4—598no—
482C2×C22⋊C4—1182no—
483C2×C22⋊C4—1182no—
484C2×C22⋊C4—1182no—
485C2×C22⋊C4—1182no—
486C2×C22⋊C4—1182no—
487C2×C22⋊C4—1184no—
488C2×C22⋊C4—1184no—
489C2×C22⋊C4—2362no—
490C2×C22⋊C4—2362no—
491C2×C22⋊C4—2362no—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—24no—
495C2×C42—42no—
496C2×C42—42no—
497C2×C42—1182no—
498C2×C42—1182no—
499C2×C42—1182no—
500C2×C42C22⋊D5914yes—
501#95—24no—
502#95—598no—
503#95—1184no—
504#95—1184no—
505#95—1184no—
506#95—1182no—
507#95—1182no—
508#95—2362no—
509#95—2362no—
510#95—2362no—
511C24—592no—
512C24—592no—
513C24—592no—
514C24—1181no—
515C24—1181no—
516C24—1181no—
517C24—1181no—
518C24—1181no—
519C24—1181no—
520C24—1181no—
521C24—1181no—
522C24—1181no—
523C24—1181no—
524C24—1181no—
525C24—1181no—
526C24C23×D5911yescharacteristic
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—592no—
550C22×C4—594no—
551C22×C4—592no—
552C22×C4—592no—
553C22×C4—1181no—
554C22×C4—1181no—
555C22×C4—1181no—
556C22×C4—1181no—
557C22×C4—1181no—
558C22×C4—1182no—
559C22×C4—1181no—
560C22×C4—1181no—
561C22×C4—1182no—
562C22×C4—1181no—
563C22×C4—1181no—
564C22×C4—1182no—
565C22×C4—1181no—
566C22×C4—1181no—
567C22×C4—1181no—
568C22×C4—1181no—
569C22×C4—1182no—
570C22×C4—1181no—
571C22×C4—1181no—
572C22×C4—1182no—
573C22×C4—1181no—
574C22×C4—1181no—
575C22×C4—1182no—
576C22×C4—1181no—
577C22×C4—1188no—
578C22×C4—1188no—
579C22×C4—1188no—
580C22×C4—1182no—
581C22×C4—1182no—
582C22×C4—1182no—
583C22×C4—1182no—
584C22×C4—1182no—
585C22×C4—1182no—
586C22×C4—1182no—
587C22×C4—2364no—
588C22×C4—2364no—
589C22×C4—2364no—
590C22×C4—2364no—
591C22×C4C2×C4×D5914yes—
592C22×C4C2×C4×D5912yes—
593C22×C4C2×D23614yes—
594C22×C4C2×D23612yes—
595C22×C4#1174568512yes—
596C22×C4#1174568512yes—
597C22×C4#1174568512yes—
598C22×C4#1174568512yes—
599C22×C4Q8×D5912yes—
600C22×C4#1174568912yes—
601C22×C4C2×C22⋊D5912yes—
602C22×C4C2×C22⋊D5912yes—
603C22×C4C2×C22⋊D5912yes—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—1188no—
607C4⋊C4—2368no—
608C4⋊C4—2364no—
609C22⋊C4—1188no—
610C22⋊C4—1188no—
611C22⋊C4—2368no—
612C22⋊C4—2368no—
613C42—28no—
614C42—48no—
615C42—2364no—
616C23—594no—
617C23—1182no—
618C23—1182no—
619C23—1182no—
620C23—1182no—
621C23—1182no—
622C23—1182no—
623C23—1182no—
624C23—1182no—
625C23—1182no—
626C23—1182no—
627C23—1182no—
628C23—1182no—
629C23—1182no—
630C23—1182no—
631C23—1182no—
632C23—1182no—
633C23—1182no—
634C23—1182no—
635C23—2361no—
636C23—2361no—
637C23—2361no—
638C23—2361no—
639C23—2361no—
640C23—2361no—
641C23—2361no—
642C23—2361no—
643C23—2361no—
644C23—2361no—
645C23—2361no—
646C23—2361no—
647C23—2361no—
648C23—2361no—
649C23—2361no—
650C23—2361no—
651C23C22×C4×D5911yescharacteristic
652C23C22×C22⋊D5911yescharacteristic
653C23C22×D23611yescharacteristic
654C23C2×Q8×D5911yescharacteristic
655C23#41×D5911yescharacteristic
656C23#41×D5911yescharacteristic
657C23C2×#1174568511yescharacteristic
658C23C2×#1174568511yescharacteristic
659C23C2×#1174568511yescharacteristic
660C23C2×#1174568511yescharacteristic
661C23C2×#1174568911yescharacteristic
662C23#1427377211yescharacteristic
663C23#1427377211yescharacteristic
664C23#1427377311yescharacteristic
665C23#1427377411yescharacteristic
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—1182no—
694C2×C4—1182no—
695C2×C4—1182no—
696C2×C4—1182no—
697C2×C4—1182no—
698C2×C4—1182no—
699C2×C4—1182no—
700C2×C4—1182no—
701C2×C4—1184no—
702C2×C4—1182no—
703C2×C4—1184no—
704C2×C4—1184no—
705C2×C4—2362no—
706C2×C4—2362no—
707C2×C4—2362no—
708C2×C4—2362no—
709C2×C4—2362no—
710C2×C4—2362no—
711C2×C4—2362no—
712C2×C4—2361no—
713C2×C4—2361no—
714C2×C4—2361no—
715C2×C4—2361no—
716C2×C4—2361no—
717C2×C4—2361no—
718C2×C4—2361no—
719C2×C4—2361no—
720C2×C4—2362no—
721C2×C4—2361no—
722C2×C4—2361no—
723C2×C4—2362no—
724C2×C4—2362no—
725C2×C4—2361no—
726C2×C4—2362no—
727C2×C4—2361no—
728C2×C4—23616no—
729C2×C4#1427368414yes—
730C2×C4C4×C22⋊D5914yes—
731C2×C4C4×D23614yes—
732C2×C4#1427370114yes—
733C2×C4#1427370314yes—
734C2×C4#1427371014yes—
735C2×C4#1427371514yes—
736C2×C4#1427372114yes—
737C22—1184no—
738C22—1184no—
739C22—1184no—
740C22—2362no—
741C22—2362no—
742C22—2362no—
743C22—2362no—
744C22—2362no—
745C22—2362no—
746C22—2362no—
747C22—2362no—
748C22—2362no—
749C22—2362no—
750C22—2362no—
751C22—2362no—
752C22C2×#1427368411yescharacteristic
753C22C2×C4×C22⋊D5911yescharacteristic
754C22C2×C4×D23611yescharacteristic
755C22C4×Q8×D5911yescharacteristic
756C22C4×#1174568911yescharacteristic
757C22#1683787411yescharacteristic
758C22#1683788111yescharacteristic
759C22C2×#1427370111yescharacteristic
760C22C2×#1427370311yescharacteristic
761C22C2×#1427371011yescharacteristic
762C22#1683790911yescharacteristic
763C22C2×#1427371511yescharacteristic
764C22C2×#1427372111yescharacteristic
765C22#1683793911yescharacteristic
766C22#1683795611yescharacteristic
767C22#1683796911yescharacteristic
768C22#1683798011yescharacteristic
769C22#1683800311yescharacteristic
770C22#1683801711yescharacteristic
771C22#1683804711yescharacteristic
772C22#1683804711yescharacteristic
773C22Q8×D23611yescharacteristic
774C22#1683807411yescharacteristic
775C22#1683809111yescharacteristic
776C22#1683809611yescharacteristic
777C22#1683810011yescharacteristic
778C22#1683810011yescharacteristic
779C22#1683810211yescharacteristic
780C22#1683810211yescharacteristic
781C22#1683810711yescharacteristic
782C22#1683810711yescharacteristic
783C22#1683811211yescharacteristic
784C22#1683811511yescharacteristic
785C22#1683812011yescharacteristic
786C22#1683812511yescharacteristic
787C4—24no—
788C4—44no—
789C4—44no—
790C4—42no—
791C4—4722no—
792C4—2362no—
793C4—2362no—
794C4—2362no—
795C4—2364no—
796C4#1683729318yes—
797C2—2364no—
798C2C2×#1683729311yescharacteristic
799C2C4×#1427370311yescharacteristic
800C2#2142678311yescharacteristic
801C2#2142696911yescharacteristic
802C2#2142698511yescharacteristic
803C2#2142710311yescharacteristic
804C2#2142713611yescharacteristic
805C2#2142838711yescharacteristic
806C2#2142840711yescharacteristic
807C2#2142844211yescharacteristic
808C2#2142846411yescharacteristic
809C2#2142849011yescharacteristic
810C2#2142852311yescharacteristic
811C2#2142899311yescharacteristic
812C2#2142901411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C4×C4⋊C4×C59C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenterC2×C4×C4⋊C4D59
hypocenterC59#13993
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16837298C2semidirect
5. #21422356C2semidirect
8. #21422329C2semidirect
9. #21422326C2semidirect
10. #21422325C2semidirect
11. C2×C4×C4⋊C4×C59C2semidirect
23. #16837259C4semidirect
394. C2×C4×C4⋊C4D59semidirect
446. C59#13993semidirect

Maximal subgroups

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

subgroupindex
C2×#168372982
C2×#168372592
C2×C4×(C2×D59)⋊C42
#214223562
#214223402
#214223342
#214223292
#214223262
#214223252
C2×C4×C4⋊C4×C592
#1399359