Finite Group Databasebeta

← #28516587

Subgroups — #28516587

Order 15104.

1398 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837294C211yesmaximal, characteristic
2C2×#16837293C211yesmaximal, characteristic
3C2×#16837268C211yesmaximal, characteristic, complemented
4#21422360C211yesmaximal, characteristic, complemented
5#21422354C211yesmaximal, characteristic, complemented
6#21422344C211yesmaximal, characteristic
7#21422342C211yesmaximal, characteristic
8#21422340C211yesmaximal, characteristic
9#21422340C211yesmaximal, characteristic
10#21422332C211yesmaximal, characteristic
11#21422330C211yesmaximal, characteristic, complemented
12#21422327C211yesmaximal, characteristic, complemented
13Dic59⋊#95C211yesmaximal, characteristic, complemented
14#21422322C211yesmaximal, characteristic, complemented
15C59×#1434C211yesmaximal, characteristic, complemented
16C22×C4⋊Dic59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×Dic59⋊C4C2211yescharacteristic
19C22×Dic59⋊C4C2211yescharacteristic
20C22×Dic59⋊C4C2211yescharacteristic
21C22×(C2×D59)⋊C4C2211yescharacteristic
22C22×(C2×D59)⋊C4C2211yescharacteristic
23C22×(C2×D59)⋊C4C2211yescharacteristic
24C22×(C2×D59)⋊C4C2211yescharacteristic
25C22×(C2×D59)⋊C4C2211yescharacteristic
26C22×(C2×D59)⋊C4C2211yescharacteristic
27C22×(C2×D59)⋊C4C2211yescharacteristic
28C22×C4×Dic59C2211yescharacteristic
29C22×C4×Dic59C2211yescharacteristic
30#16837294—24no—
31#16837293C418yescomplemented
32#16837268—24no—
33C2×C59⋊#95C2211yescharacteristic
34C2×C59⋊#95C2211yescharacteristic
35C2×C59⋊#95C2211yescharacteristic
36C2×C59⋊#95C2211yescharacteristic
37C2×C59⋊#95C2211yescharacteristic
38C2×C59⋊#95C2211yescharacteristic
39C2×C59⋊#95C2211yescharacteristic
40C2×C59⋊#95C2211yescharacteristic
41C2×C59⋊#95C2211yescharacteristic
42C2×C59⋊#95C2211yescharacteristic
43C2×C59⋊#95C2211yescharacteristic
44C2×C59⋊#95C2211yescharacteristic
45C2×C59⋊#95C2211yescharacteristic
46C2×C59⋊#95C2211yescharacteristic
47C22×C42×C59C2211yescharacteristic
48C2×#95×C59C2211yescharacteristic
49C2×#95×C59C2211yescharacteristic
50C2×#95×C59C2211yescharacteristic
51C2×#95×C59C2211yescharacteristic
52C2×#95×C59C2211yescharacteristic
53C2×#95×C59C2211yescharacteristic
54C24×D59C2311yescharacteristic
55C23×Dic59C2311yescharacteristic
56C23×Dic59C2311yescharacteristic
57C23×Dic59C2311yescharacteristic
58C23×Dic59C2311yescharacteristic
59C23×Dic59C2311yescharacteristic
60C23×Dic59C2311yescharacteristic
61C23×Dic59C2311yescharacteristic
62C2×C4⋊Dic59—22no—
63C2×C4⋊Dic59—41no—
64C2×C4⋊Dic59—41no—
65C2×C4⋊Dic59—41no—
66C2×C4⋊Dic59—41no—
67C2×C4⋊Dic59D414yes—
68C2×Dic59⋊C4—22no—
69C2×Dic59⋊C4—41no—
70C2×Dic59⋊C4—41no—
71C2×Dic59⋊C4—41no—
72C2×Dic59⋊C4—41no—
73C2×Dic59⋊C4—41no—
74C2×Dic59⋊C4—41no—
75C2×Dic59⋊C4—41no—
76C2×Dic59⋊C4C2×C414yes—
77C2×(C2×D59)⋊C4—22no—
78C2×(C2×D59)⋊C4—22no—
79C2×(C2×D59)⋊C4—22no—
80C2×(C2×D59)⋊C4—22no—
81C2×(C2×D59)⋊C4—22no—
82C2×(C2×D59)⋊C4—22no—
83C2×(C2×D59)⋊C4—22no—
84C2×(C2×D59)⋊C4—22no—
85C2×(C2×D59)⋊C4—41no—
86C2×(C2×D59)⋊C4—41no—
87C2×(C2×D59)⋊C4—41no—
88C2×(C2×D59)⋊C4—41no—
89C2×(C2×D59)⋊C4—41no—
90C2×(C2×D59)⋊C4—41no—
91C2×(C2×D59)⋊C4—41no—
92C2×(C2×D59)⋊C4—41no—
93C2×(C2×D59)⋊C4—41no—
94C2×(C2×D59)⋊C4—41no—
95C2×(C2×D59)⋊C4C2×C414yes—
96C2×(C2×D59)⋊C4C2×C414yes—
97C2×(C2×D59)⋊C4C2×C414yes—
98C2×C4×Dic59—22no—
99C2×C4×Dic59—22no—
100C2×C4×Dic59—22no—
101C2×C4×Dic59—41no—
102C2×C4×Dic59—41no—
103C2×C4×Dic59—41no—
104C59⋊#95—22no—
105C59⋊#95—22no—
106C59⋊#95—22no—
107C59⋊#95—22no—
108C59⋊#95—22no—
109C59⋊#95—22no—
110C59⋊#95—22no—
111C59⋊#95—22no—
112C59⋊#95—41no—
113C59⋊#95—41no—
114C59⋊#95—41no—
115C59⋊#95—41no—
116C59⋊#95C2×C414yes—
117C59⋊#95C2×C414yes—
118C23×C4×C59C2311yescharacteristic
119C23×C4×C59C2311yescharacteristic
120C23×C4×C59C2311yescharacteristic
121C23×C4×C59C2311yescharacteristic
122C23×C4×C59C2311yescharacteristic
123C23×C4×C59C2311yescharacteristic
124C23×C4×C59C2311yescharacteristic
125C2×C42×C59—22no—
126C2×C42×C59—22no—
127C2×C42×C59C2×C414yes—
128#95×C59—22no—
129#95×C59—22no—
130#95×C59—22no—
131#95×C59—22no—
132#95×C59—41no—
133#95×C59—41no—
134C24×C59C2411yescharacteristic
135C23×D59—21no—
136C23×D59—21no—
137C23×D59—21no—
138C23×D59—21no—
139C23×D59—21no—
140C23×D59—21no—
141C23×D59—21no—
142C23×D59—21no—
143C23×D59—21no—
144C23×D59—21no—
145C23×D59—21no—
146C23×D59—21no—
147C23×D59—21no—
148C23×D59—21no—
149C23×D59C22×C412yes—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59C22×C412yes—
193C22×C4×C59C22×C412yes—
194C22×C4×C59C22×C412yes—
195C22×C4×C59C2×D412yes—
196C22×C4×C59#4112yes—
197C22×C4×C59#4112yes—
198C22×C4×C59#4112yes—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C22×Dic59—21no—
217C22×Dic59—21no—
218C22×Dic59—21no—
219C22×Dic59—21no—
220C22×Dic59—21no—
221C22×Dic59—21no—
222C22×Dic59—21no—
223C22×Dic59—21no—
224C22×Dic59—21no—
225C22×Dic59—21no—
226C22×Dic59—21no—
227C22×Dic59—21no—
228C22×Dic59—21no—
229C22×Dic59—21no—
230C22×Dic59—21no—
231C22×Dic59—21no—
232C22×Dic59—21no—
233C22×Dic59—21no—
234C22×Dic59—21no—
235C22×Dic59—21no—
236C22×Dic59—21no—
237C22×Dic59—21no—
238C22×Dic59—21no—
239C22×Dic59—21no—
240C22×Dic59—21no—
241C22×Dic59C22×C412yes—
242C22×Dic59C22×C412yes—
243C22×Dic59C22×C412yes—
244C22×Dic59C2×D412yes—
245C22×Dic59C2×D412yes—
246C22×Dic59#4112yes—
247C22×Dic59#4112yes—
248C42×C59—28no—
249(C2×D59)⋊C4—28no—
250(C2×D59)⋊C4—28no—
251(C2×D59)⋊C4—44no—
252(C2×D59)⋊C4—44no—
253(C2×D59)⋊C4—44no—
254(C2×D59)⋊C4—44no—
255(C2×D59)⋊C4—44no—
256C4⋊Dic59—44no—
257C4⋊Dic59—44no—
258Dic59⋊C4—44no—
259Dic59⋊C4—44no—
260Dic59⋊C4—44no—
261C4×Dic59—44no—
262C4×Dic59—44no—
263C23×C59C23×C411yescharacteristic
264C23×C59C22×D411yescharacteristic
265C23×C59C2×#4111yescharacteristic
266C23×C59C2×#4111yescharacteristic
267C23×C59C2×#4111yescharacteristic
268C23×C59C2×#4111yescharacteristic
269C23×C59C2×#4111yescharacteristic
270C23×C59H(5,𝔽2)11yescharacteristic
271C23×C59H(5,𝔽2)11yescharacteristic
272C23×C59H(5,𝔽2)11yescharacteristic
273C23×C59H(5,𝔽2)11yescharacteristic
274C23×C59H(5,𝔽2)11yescharacteristic
275C23×C592−1+411yescharacteristic
276C23×C592−1+411yescharacteristic
277C23×C592−1+411yescharacteristic
278C22×D59—22no—
279C22×D59—22no—
280C22×D59—22no—
281C22×D59—22no—
282C22×D59—22no—
283C22×D59—22no—
284C22×D59—22no—
285C22×D59—41no—
286C22×D59—41no—
287C22×D59—41no—
288C22×D59—41no—
289C22×D59—41no—
290C22×D59—41no—
291C22×D59—41no—
292C22×D59—41no—
293C22×D59—41no—
294C22×D59—41no—
295C22×D59—41no—
296C22×D59—41no—
297C22×D59—41no—
298C22×D59—41no—
299C22×D59—41no—
300C22×D59—41no—
301C22×D59—41no—
302C22×D59—41no—
303C22×D59—41no—
304C22×D59—41no—
305C22×D59—41no—
306C22×D59—41no—
307C22×D59—41no—
308C22×D59—41no—
309C22×D59—41no—
310C22×D59—41no—
311C22×D59—41no—
312C22×D59—41no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59—22no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—22no—
329C2×C4×C59—22no—
330C2×C4×C59—22no—
331C2×C4×C59—41no—
332C2×C4×C59—41no—
333C2×C4×C59—41no—
334C2×C4×C59—41no—
335C2×C4×C59—41no—
336C2×C4×C59—41no—
337C2×C4×C59—41no—
338C2×C4×C59—41no—
339C2×C4×C59—41no—
340C2×C4×C59—41no—
341C2×C4×C59—41no—
342C2×C4×C59—41no—
343C2×C4×C59—41no—
344C2×C4×C59—41no—
345C2×C4×C59—41no—
346C2×C4×C59—41no—
347C2×C4×C59—41no—
348C2×C4×C59—41no—
349C2×C4×C59—41no—
350C2×C4×C59—41no—
351C2×C4×C59—41no—
352C2×C4×C59—41no—
353C2×C4×C59—41no—
354C2×C4×C59—41no—
355C2×C4×C59—41no—
356C2×C4×C59—41no—
357C2×C4×C59—41no—
358C2×C4×C59—41no—
359C2×C4×C59—41no—
360C2×C4×C59—41no—
361C2×C4×C59C4×D414yes—
362C2×Dic59—22no—
363C2×Dic59—22no—
364C2×Dic59—22no—
365C2×Dic59—22no—
366C2×Dic59—22no—
367C2×Dic59—22no—
368C2×Dic59—22no—
369C2×Dic59—22no—
370C2×Dic59—22no—
371C2×Dic59—22no—
372C2×Dic59—22no—
373C2×Dic59—22no—
374C2×Dic59—22no—
375C2×Dic59—22no—
376C2×Dic59—22no—
377C2×Dic59—22no—
378C2×Dic59—22no—
379C2×Dic59—22no—
380C2×Dic59—41no—
381C2×Dic59—41no—
382C2×Dic59—41no—
383C2×Dic59—41no—
384C2×Dic59—41no—
385C2×Dic59—41no—
386C2×Dic59—41no—
387C2×Dic59—41no—
388C2×Dic59—41no—
389C2×Dic59—41no—
390C2×Dic59—41no—
391C2×Dic59—41no—
392C2×Dic59—41no—
393C2×Dic59—41no—
394C2×Dic59—41no—
395C2×Dic59—41no—
396C2×Dic59—41no—
397C2×Dic59—41no—
398C2×Dic59—41no—
399C2×Dic59—41no—
400C2×Dic59—41no—
401C2×Dic59—41no—
402C2×Dic59—41no—
403C2×Dic59—41no—
404C2×Dic59—41no—
405C2×Dic59—41no—
406C2×Dic59—41no—
407C2×Dic59—41no—
408C2×Dic59—41no—
409C2×Dic59—41no—
410C2×Dic59#11714yes—
411#14399—591nomaximal, Sylow
412C22×C59C2×#11711yescharacteristic
413C22×C59C2×C4×D411yescharacteristic
414C22×C59C4×#4111yescharacteristic
415C22×C59#51811yescharacteristic
416C22×C59#52011yescharacteristic
417C22×C59#52011yescharacteristic
418C22×C59#52011yescharacteristic
419C22×C59#53411yescharacteristic
420C22×C59#53611yescharacteristic
421C22×C59#53811yescharacteristic
422C22×C59#53811yescharacteristic
423C22×C59#53811yescharacteristic
424C22×C59#53911yescharacteristic
425C22×C59#53911yescharacteristic
426C22×C59#53911yescharacteristic
427C22×C59#53911yescharacteristic
428C22×C59#53911yescharacteristic
429C22×C59#54111yescharacteristic
430C22×C59#54211yescharacteristic
431C22×C59#54611yescharacteristic
432C22×C59#54711yescharacteristic
433C22×C59#55011yescharacteristic
434C22×C59#55011yescharacteristic
435C22×C59#55211yescharacteristic
436C22×C59#55211yescharacteristic
437C22×C59#55311yescharacteristic
438C22×C59#55511yescharacteristic
439C22×C59#55511yescharacteristic
440C22×C59#55511yescharacteristic
441C22×C59#55511yescharacteristic
442C22×C59#55611yescharacteristic
443C22×C59H(3,𝔽4)11yescharacteristic
444C22×C59#56211yescharacteristic
445C22×C59#56211yescharacteristic
446C22×C59#56311yescharacteristic
447C2×D59—42no—
448C2×D59—42no—
449C2×D59—42no—
450C2×D59—42no—
451C2×D59—42no—
452C2×D59—42no—
453C2×D59—42no—
454C2×D59—81no—
455C2×D59—81no—
456C2×D59—81no—
457C2×D59—81no—
458C2×D59—81no—
459C2×D59—81no—
460C2×D59—81no—
461C2×D59—81no—
462C4×C59—24no—
463C4×C59—42no—
464C4×C59—42no—
465C4×C59—42no—
466C4×C59—42no—
467C4×C59—81no—
468C4×C59—81no—
469Dic59—24no—
470Dic59—42no—
471Dic59—42no—
472Dic59—42no—
473Dic59—42no—
474Dic59—81no—
475Dic59—81no—
476C2×#388—591no—
477C2×#388—591no—
478C2×#382—591no—
479#1444—591no—
480#1442—591no—
481#1440—591no—
482#1439—591no—
483#1439—591no—
484#1439—591no—
485#1437—591no—
486#1436—591no—
487#1436—591no—
488C4⋊#95—591no—
489#1434—591no—
490#1434D5911yescharacteristic, complemented
491C2×C59#231811yescharacteristic
492C2×C59#232211yescharacteristic
493C2×C59#233411yescharacteristic
494C2×C59#234611yescharacteristic
495C2×C59#235411yescharacteristic
496C2×C59#236311yescharacteristic
497C2×C59#237911yescharacteristic
498C2×C59#268611yescharacteristic
499C2×C59#269411yescharacteristic
500C2×C59#272111yescharacteristic
501C2×C59#273311yescharacteristic
502C2×C59#277511yescharacteristic
503C2×C59#278111yescharacteristic
504C2×C59#278311yescharacteristic
505C2×C59#278511yescharacteristic
506D59—82no—
507C22×C4⋊C4—591no—
508C22×C4⋊C4—591no—
509C22×C4⋊C4—591no—
510C22×C4⋊C4—591no—
511C22×C4⋊C4—591no—
512C22×C22⋊C4—591no—
513C22×C22⋊C4—591no—
514C22×C22⋊C4—591no—
515C22×C22⋊C4—591no—
516C22×C22⋊C4—591no—
517C22×C22⋊C4—591no—
518C22×C22⋊C4—591no—
519C22×C42—591no—
520C22×C42—591no—
521C22×C42C2×D5911yescharacteristic
522#388—598no—
523#388—1184no—
524#382—1184no—
525C2×#95—591no—
526C2×#95—591no—
527C2×#95—591no—
528C2×#95—591no—
529C2×#95—591no—
530C2×#95—591no—
531C2×#95—591no—
532C2×#95—591no—
533C2×#95—591no—
534C2×#95—591no—
535C2×#95—591no—
536C2×#95—591no—
537C2×#95—591no—
538C2×#95—591no—
539C2×#95C2×D5911yescharacteristic
540C2×#95C2×D5911yescharacteristic
541C2×#95C2×D5911yescharacteristic
542C2×#95C2×D5911yescharacteristic
543C2×#95C2×D5911yescharacteristic
544C2×#95C2×D5911yescharacteristic
545C59#1439911yescharacteristic, complemented, Sylow
546C25—591no—
547C23×C4—591no—
548C23×C4—591no—
549C23×C4—591no—
550C23×C4—591no—
551C23×C4—591no—
552C23×C4—591no—
553C23×C4—591no—
554C23×C4C22×D5911yescharacteristic
555C23×C4C22×D5911yescharacteristic
556C23×C4C22×D5911yescharacteristic
557C23×C4C22×D5911yescharacteristic
558C23×C4C22×D5911yescharacteristic
559C23×C4C22×D5911yescharacteristic
560C23×C4C22×D5911yescharacteristic
561C2×C4⋊C4—594no—
562C2×C4⋊C4—594no—
563C2×C4⋊C4—1182no—
564C2×C4⋊C4—1182no—
565C2×C4⋊C4—2361no—
566C2×C4⋊C4—2361no—
567C2×C4⋊C4—2361no—
568C2×C4⋊C4—2361no—
569C2×C4⋊C4—2361no—
570C2×C4⋊C4—2361no—
571C2×C4⋊C4—2361no—
572C2×C4⋊C4—2361no—
573C2×C4⋊C4—2361no—
574C2×C4⋊C4—2361no—
575C2×C4⋊C4—2361no—
576C2×C22⋊C4—594no—
577C2×C22⋊C4—594no—
578C2×C22⋊C4—594no—
579C2×C22⋊C4—1182no—
580C2×C22⋊C4—1182no—
581C2×C22⋊C4—1182no—
582C2×C22⋊C4—1182no—
583C2×C22⋊C4—1182no—
584C2×C22⋊C4—1182no—
585C2×C22⋊C4—1182no—
586C2×C22⋊C4—1182no—
587C2×C22⋊C4—2361no—
588C2×C22⋊C4—2361no—
589C2×C22⋊C4—2361no—
590C2×C22⋊C4—2361no—
591C2×C22⋊C4—2361no—
592C2×C22⋊C4—2361no—
593C2×C22⋊C4—2361no—
594C2×C22⋊C4—2361no—
595C2×C22⋊C4—2361no—
596C2×C22⋊C4—2361no—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—1182no—
600C2×C42—1182no—
601C2×C42—1182no—
602C2×C42—2361no—
603C2×C42—2361no—
604C2×C42—2361no—
605C2×C42C4×D5914yes—
606#95—22no—
607#95—22no—
608#95—22no—
609#95—22no—
610#95—41no—
611#95—41no—
612#95—594no—
613#95—594no—
614#95—1182no—
615#95—1182no—
616#95—1182no—
617#95—1182no—
618#95—1182no—
619#95—1182no—
620#95—1182no—
621#95—1182no—
622#95—2361no—
623#95—2361no—
624#95—2361no—
625#95—2361no—
626C24—592no—
627C24—1181no—
628C24—1181no—
629C24—1181no—
630C24—1181no—
631C24—1181no—
632C24—1181no—
633C24—1181no—
634C24—1181no—
635C24—1181no—
636C24—1181no—
637C24—1181no—
638C24—1181no—
639C24—1181no—
640C24—1181no—
641C24C23×D5911yescharacteristic
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—592no—
685C22×C4—592no—
686C22×C4—592no—
687C22×C4—592no—
688C22×C4—592no—
689C22×C4—592no—
690C22×C4—592no—
691C22×C4—1181no—
692C22×C4—1181no—
693C22×C4—1181no—
694C22×C4—1181no—
695C22×C4—1181no—
696C22×C4—1181no—
697C22×C4—1181no—
698C22×C4—1181no—
699C22×C4—1181no—
700C22×C4—1181no—
701C22×C4—1181no—
702C22×C4—1181no—
703C22×C4—1181no—
704C22×C4—1181no—
705C22×C4—1181no—
706C22×C4—1181no—
707C22×C4—1181no—
708C22×C4—1181no—
709C22×C4—1181no—
710C22×C4—1181no—
711C22×C4—1181no—
712C22×C4—1181no—
713C22×C4—1181no—
714C22×C4—1181no—
715C22×C4—1181no—
716C22×C4—1181no—
717C22×C4—1181no—
718C22×C4—1181no—
719C22×C4—1181no—
720C22×C4—1181no—
721C22×C4—1181no—
722C22×C4—1181no—
723C22×C4—1181no—
724C22×C4—1181no—
725C22×C4—1181no—
726C22×C4—1181no—
727C22×C4—1181no—
728C22×C4—1181no—
729C22×C4—1181no—
730C22×C4—1181no—
731C22×C4—1181no—
732C22×C4—1181no—
733C22×C4C2×C4×D5912yes—
734C22×C4C2×C4×D5912yes—
735C22×C4C2×C4×D5912yes—
736C22×C4#1174568512yes—
737C22×C4#1174568512yes—
738C22×C4D4×D5912yes—
739C22×C4#1174568712yes—
740C4⋊C4—2364no—
741C4⋊C4—2364no—
742C4⋊C4—2364no—
743C4⋊C4—2364no—
744C4⋊C4—2364no—
745C22⋊C4—1188no—
746C22⋊C4—1188no—
747C22⋊C4—2364no—
748C22⋊C4—2364no—
749C22⋊C4—2364no—
750C22⋊C4—2364no—
751C22⋊C4—2364no—
752C42—28no—
753C42—2364no—
754C42—2364no—
755C23—1182no—
756C23—1182no—
757C23—1182no—
758C23—1182no—
759C23—1182no—
760C23—1182no—
761C23—1182no—
762C23—2361no—
763C23—2361no—
764C23—2361no—
765C23—2361no—
766C23—2361no—
767C23—2361no—
768C23—2361no—
769C23—2361no—
770C23—2361no—
771C23—2361no—
772C23—2361no—
773C23—2361no—
774C23—2361no—
775C23—2361no—
776C23—2361no—
777C23—2361no—
778C23—2361no—
779C23—2361no—
780C23—2361no—
781C23—2361no—
782C23—2361no—
783C23—2361no—
784C23—2361no—
785C23—2361no—
786C23—2361no—
787C23—2361no—
788C23—2361no—
789C23—2361no—
790C23C22×C4×D5911yescharacteristic
791C23C2×D4×D5911yescharacteristic
792C23#41×D5911yescharacteristic
793C23#41×D5911yescharacteristic
794C23C2×#1174568711yescharacteristic
795C23C2×#1174568511yescharacteristic
796C23C2×#1174568511yescharacteristic
797C23#1427377211yescharacteristic
798C23#1427377311yescharacteristic
799C23#1427377311yescharacteristic
800C23#1427377311yescharacteristic
801C23#1427377311yescharacteristic
802C23#1427377411yescharacteristic
803C23#1427377411yescharacteristic
804C23#1427377511yescharacteristic
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—594no—
854C2×C4—1182no—
855C2×C4—1182no—
856C2×C4—1182no—
857C2×C4—1182no—
858C2×C4—1182no—
859C2×C4—1182no—
860C2×C4—1182no—
861C2×C4—1182no—
862C2×C4—1182no—
863C2×C4—1182no—
864C2×C4—1182no—
865C2×C4—1182no—
866C2×C4—1182no—
867C2×C4—1182no—
868C2×C4—1182no—
869C2×C4—1182no—
870C2×C4—1182no—
871C2×C4—1182no—
872C2×C4—2361no—
873C2×C4—2361no—
874C2×C4—2361no—
875C2×C4—2361no—
876C2×C4—2361no—
877C2×C4—2361no—
878C2×C4—2361no—
879C2×C4—2361no—
880C2×C4—2361no—
881C2×C4—2361no—
882C2×C4—2361no—
883C2×C4—2361no—
884C2×C4—2361no—
885C2×C4—2361no—
886C2×C4—2361no—
887C2×C4—2361no—
888C2×C4—2361no—
889C2×C4—2361no—
890C2×C4—2361no—
891C2×C4—2361no—
892C2×C4—2361no—
893C2×C4—2361no—
894C2×C4—2361no—
895C2×C4—2361no—
896C2×C4—2361no—
897C2×C4—2361no—
898C2×C4—2361no—
899C2×C4—2361no—
900C2×C4—2361no—
901C2×C4—2361no—
902C2×C4(C22⋊D59)⋊C414yes—
903C22—4721no—
904C22—4721no—
905C22—4721no—
906C22—4721no—
907C22—4721no—
908C22—4721no—
909C22—4721no—
910C22—4721no—
911C22—2362no—
912C22—2362no—
913C22—2362no—
914C22—2362no—
915C22—2362no—
916C22—2362no—
917C22—2362no—
918C22#117×D5911yescharacteristic
919C22C2×(C22⋊D59)⋊C411yescharacteristic
920C22C4×#1174568511yescharacteristic
921C22#1683787611yescharacteristic
922C22#1683788211yescharacteristic
923C22#1683788211yescharacteristic
924C22#1683788311yescharacteristic
925C22#1683796311yescharacteristic
926C22#1683797411yescharacteristic
927C22#1683798511yescharacteristic
928C22#1683799111yescharacteristic
929C22#1683799111yescharacteristic
930C22#1683799311yescharacteristic
931C22#1683799311yescharacteristic
932C22#1683799411yescharacteristic
933C22#1683799611yescharacteristic
934C22#1683799611yescharacteristic
935C22#1683801011yescharacteristic
936C22#1683802411yescharacteristic
937C22#1683804811yescharacteristic
938C22#1683805411yescharacteristic
939C22#1683807011yescharacteristic
940C22#1683807311yescharacteristic
941C22#1683808511yescharacteristic
942C22#1683808511yescharacteristic
943C22#1683809811yescharacteristic
944C22#1683811511yescharacteristic
945C22#1683811511yescharacteristic
946C22#1683811611yescharacteristic
947C22#1683811711yescharacteristic
948C22#1683812311yescharacteristic
949C22#1683814411yescharacteristic
950C22#1683814611yescharacteristic
951C22#1683815011yescharacteristic
952C22#1683815611yescharacteristic
953C4—24no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—81no—
959C4—81no—
960C4—1184no—
961C4—4721no—
962C4—4721no—
963C4—2362no—
964C4—2362no—
965C4—2362no—
966C4—2362no—
967C2—4722no—
968C2#2142672711yescharacteristic
969C2#2142676211yescharacteristic
970C2#2142687111yescharacteristic
971C2#2142698211yescharacteristic
972C2#2142704011yescharacteristic
973C2#2142713211yescharacteristic
974C2#2142726711yescharacteristic
975C2#2143050511yescharacteristic
976C2#2143061911yescharacteristic
977C2#2143099211yescharacteristic
978C2#2143112311yescharacteristic
979C2#2143166311yescharacteristic
980C2#2143175911yescharacteristic
981C2#2143178311yescharacteristic
982C2#2143180111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×#1434C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenter#1434D59
hypocenterC59#14399
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#16837268C2semidirect
4. #21422360C2semidirect
5. #21422354C2semidirect
11. #21422330C2semidirect
12. #21422327C2semidirect
13. Dic59⋊#95C2semidirect
14. #21422322C2semidirect
15. C59×#1434C2semidirect
31. #16837293C4semidirect
490. #1434D59semidirect
545. C59#14399semidirect

Maximal subgroups

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

subgroupindex
C2×#168372942
C2×#168372932
C2×#168372682
#214223602
#214223542
#214223442
#214223422
#214223402
#214223322
#214223302
#214223272
Dic59⋊#952
#214223222
C59×#14342
#1439959