Finite Group Databasebeta

← #28519583

Subgroups — #28519583

Order 15104.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837317C211yesmaximal, characteristic
2#21422362C211yesmaximal, characteristic, complemented
3#21422357C211yesmaximal, characteristic, complemented
4#21422350C211yesmaximal, characteristic, complemented
5#21422344C211yesmaximal, characteristic, complemented
6#21422343C211yesmaximal, characteristic, complemented
7#21422342C211yesmaximal, characteristic, complemented
8#21422341C211yesmaximal, characteristic, complemented
9#21422340C211yesmaximal, characteristic, complemented
10#21422339C211yesmaximal, characteristic, complemented
11#21422335C211yesmaximal, characteristic
12#21422335C211yesmaximal, characteristic
13#21422334C211yesmaximal, characteristic, complemented
14#21422329C211yesmaximal, characteristic, complemented
15C59×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×Dic59⋊C4C2211yescharacteristic
19C22×Dic59⋊C4C2211yescharacteristic
20C22×C22⋊Dic59C2211yescharacteristic
21C22×C22⋊Dic59C2211yescharacteristic
22C22×C22⋊Dic59C2211yescharacteristic
23C22×(C2×D59)⋊C4C2211yescharacteristic
24C22×(C2×D59)⋊C4C2211yescharacteristic
25C22×(C2×D59)⋊C4C2211yescharacteristic
26C22×(C2×D59)⋊C4C2211yescharacteristic
27C22×(C2×D59)⋊C4C2211yescharacteristic
28C22×(C2×D59)⋊C4C2211yescharacteristic
29#16837317C418yescomplemented
30C2×C59⋊#95C2211yescharacteristic
31C2×C59⋊#95C2211yescharacteristic
32C2×C59⋊#95C2211yescharacteristic
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
45C22×C22⋊C4×C59C2211yescharacteristic
46C22×C22⋊C4×C59C2211yescharacteristic
47C22×C22⋊C4×C59C2211yescharacteristic
48C22×C42×C59C2211yescharacteristic
49C2×#95×C59C2211yescharacteristic
50C2×#95×C59C2211yescharacteristic
51C2×#95×C59C2211yescharacteristic
52C24×D59C2311yescharacteristic
53C22×C22⋊D59—41no—
54C22×C22⋊D59—41no—
55C22×C22⋊D59—41no—
56C22×C22⋊D59—41no—
57C22×C22⋊D59—41no—
58C22×C22⋊D59—41no—
59C22×C22⋊D59C2×C414yes—
60C23×Dic59C2311yescharacteristic
61C23×Dic59C2311yescharacteristic
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2311yescharacteristic
64C23×Dic59C2311yescharacteristic
65C23×Dic59C2311yescharacteristic
66C23×Dic59C2311yescharacteristic
67C2×C4⋊Dic59—41no—
68C2×C4⋊Dic59—41no—
69C2×C4⋊Dic59—41no—
70C2×Dic59⋊C4—22no—
71C2×Dic59⋊C4—41no—
72C2×Dic59⋊C4—41no—
73C2×Dic59⋊C4—41no—
74C2×Dic59⋊C4—41no—
75C2×Dic59⋊C4C2×C414yes—
76C2×C22⋊Dic59—41no—
77C2×C22⋊Dic59—41no—
78C2×C22⋊Dic59—41no—
79C2×C22⋊Dic59—41no—
80C2×C22⋊Dic59—41no—
81C2×C22⋊Dic59—41no—
82C2×C22⋊Dic59—41no—
83C2×C22⋊Dic59—41no—
84C2×C22⋊Dic59C2×C414yes—
85C2×(C2×D59)⋊C4—22no—
86C2×(C2×D59)⋊C4—22no—
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)⋊C4—41no—
96C2×(C2×D59)⋊C4—41no—
97C2×(C2×D59)⋊C4—41no—
98C2×(C2×D59)⋊C4—41no—
99C2×(C2×D59)⋊C4—41no—
100C2×(C2×D59)⋊C4—41no—
101C2×(C2×D59)⋊C4C2×C414yes—
102C2×(C2×D59)⋊C4C2×C414yes—
103C59⋊#95—22no—
104C59⋊#95—41no—
105C59⋊#95—41no—
106C59⋊#95—41no—
107C59⋊#95—41no—
108C59⋊#95—41no—
109C59⋊#95—41no—
110C59⋊#95—41no—
111C59⋊#95—41no—
112C59⋊#95—41no—
113C59⋊#95—41no—
114C59⋊#95—41no—
115C59⋊#95—41no—
116C59⋊#95—41no—
117C59⋊#95C2×C414yes—
118C25×C59C2311yescharacteristic
119C23×C4×C59C2311yescharacteristic
120C23×C4×C59C2311yescharacteristic
121C23×C4×C59C2311yescharacteristic
122C23×C4×C59C2311yescharacteristic
123C23×C4×C59C2311yescharacteristic
124C23×C4×C59C2311yescharacteristic
125C2×C22⋊C4×C59—22no—
126C2×C22⋊C4×C59—22no—
127C2×C22⋊C4×C59—41no—
128C2×C22⋊C4×C59—41no—
129C2×C22⋊C4×C59—41no—
130C2×C22⋊C4×C59—41no—
131C2×C22⋊C4×C59—41no—
132C2×C22⋊C4×C59—41no—
133C2×C22⋊C4×C59C2×C414yes—
134C2×C42×C59—41no—
135C2×C42×C59—41no—
136C2×C42×C59—41no—
137#95×C59—41no—
138#95×C59—41no—
139#95×C59—41no—
140C24×C59—21no—
141C24×C59—21no—
142C24×C59—21no—
143C24×C59—21no—
144C24×C59—21no—
145C24×C59—21no—
146C24×C59—21no—
147C24×C59—21no—
148C24×C59—21no—
149C24×C59—21no—
150C24×C59—21no—
151C24×C59—21no—
152C24×C59—21no—
153C24×C59—21no—
154C24×C59C22×C412yes—
155C24×C59C2411yescharacteristic
156C23×D59—21no—
157C23×D59—21no—
158C23×D59—21no—
159C23×D59—21no—
160C23×D59—21no—
161C23×D59—21no—
162C23×D59—21no—
163C23×D59—21no—
164C23×D59—21no—
165C23×D59—21no—
166C23×D59—21no—
167C23×D59—21no—
168C23×D59—21no—
169C23×D59—21no—
170C23×D59C22×C412yes—
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×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59C22×C412yes—
210C22×C4×C59C22×C412yes—
211C22×C4×C59#4112yes—
212C22×C4×C59#4112yes—
213C2×C22⋊D59—44no—
214C2×C22⋊D59—44no—
215C2×C22⋊D59—44no—
216C2×C22⋊D59—44no—
217C2×C22⋊D59—44no—
218C2×C22⋊D59—44no—
219C2×C22⋊D59—44no—
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×Dic59—21no—
242C22×Dic59—21no—
243C22×Dic59—21no—
244C22×Dic59—21no—
245C22×Dic59—21no—
246C22×Dic59—21no—
247C22×Dic59—21no—
248C22×Dic59—21no—
249C22×Dic59—21no—
250C22×Dic59—21no—
251C22×Dic59—21no—
252C22×Dic59—21no—
253C22×Dic59—21no—
254C22×Dic59—21no—
255C22×Dic59—21no—
256C22×Dic59—21no—
257C22×Dic59—21no—
258C22×Dic59—21no—
259C22×Dic59—21no—
260C22×Dic59—21no—
261C22×Dic59—21no—
262C22×Dic59—21no—
263C22×Dic59—21no—
264C22×Dic59—21no—
265C22×Dic59—21no—
266C22×Dic59C22×C412yes—
267C22×Dic59C22×C412yes—
268C22×Dic59C22×C412yes—
269C22⋊C4×C59—44no—
270C22⋊C4×C59—44no—
271C22⋊C4×C59—44no—
272C42×C59—44no—
273C22⋊Dic59—44no—
274C22⋊Dic59—44no—
275C22⋊Dic59—44no—
276(C2×D59)⋊C4—44no—
277(C2×D59)⋊C4—44no—
278(C2×D59)⋊C4—44no—
279(C2×D59)⋊C4—44no—
280(C2×D59)⋊C4—44no—
281(C2×D59)⋊C4—44no—
282C4⋊Dic59—44no—
283Dic59⋊C4—44no—
284Dic59⋊C4—44no—
285C23×C59—22no—
286C23×C59—22no—
287C23×C59—22no—
288C23×C59—22no—
289C23×C59—22no—
290C23×C59—22no—
291C23×C59—22no—
292C23×C59—41no—
293C23×C59—41no—
294C23×C59—41no—
295C23×C59—41no—
296C23×C59—41no—
297C23×C59—41no—
298C23×C59—41no—
299C23×C59—41no—
300C23×C59—41no—
301C23×C59—41no—
302C23×C59—41no—
303C23×C59—41no—
304C23×C59—41no—
305C23×C59—41no—
306C23×C59—41no—
307C23×C59—41no—
308C23×C59—41no—
309C23×C59—41no—
310C23×C59—41no—
311C23×C59—41no—
312C23×C59—41no—
313C23×C59—41no—
314C23×C59—41no—
315C23×C59—41no—
316C23×C59—41no—
317C23×C59—41no—
318C23×C59—41no—
319C23×C59—41no—
320C23×C59C23×C411yescharacteristic
321C23×C59C2×#4111yescharacteristic
322C23×C59C2×#4111yescharacteristic
323C23×C59H(5,𝔽2)11yescharacteristic
324C23×C59H(5,𝔽2)11yescharacteristic
325C23×C59H(5,𝔽2)11yescharacteristic
326C23×C59H(5,𝔽2)11yescharacteristic
327C23×C59H(5,𝔽2)11yescharacteristic
328C23×C59H(5,𝔽2)11yescharacteristic
329C23×C59H(5,𝔽2)11yescharacteristic
330C23×C59H(5,𝔽2)11yescharacteristic
331C23×C59H(5,𝔽2)11yescharacteristic
332C23×C59H(5,𝔽2)11yescharacteristic
333C23×C592−1+411yescharacteristic
334C23×C592−1+411yescharacteristic
335C22×D59—22no—
336C22×D59—22no—
337C22×D59—22no—
338C22×D59—22no—
339C22×D59—22no—
340C22×D59—22no—
341C22×D59—22no—
342C22×D59—41no—
343C22×D59—41no—
344C22×D59—41no—
345C22×D59—41no—
346C22×D59—41no—
347C22×D59—41no—
348C22×D59—41no—
349C22×D59—41no—
350C22×D59—41no—
351C22×D59—41no—
352C22×D59—41no—
353C22×D59—41no—
354C22×D59—41no—
355C22×D59—41no—
356C22×D59—41no—
357C22×D59—41no—
358C22×D59—41no—
359C22×D59—41no—
360C22×D59—41no—
361C22×D59—41no—
362C22×D59—41no—
363C22×D59—41no—
364C22×D59—41no—
365C22×D59—41no—
366C22×D59—41no—
367C22×D59—41no—
368C22×D59—41no—
369C22×D59—41no—
370C2×C4×C59—22no—
371C2×C4×C59—22no—
372C2×C4×C59—22no—
373C2×C4×C59—22no—
374C2×C4×C59—22no—
375C2×C4×C59—22no—
376C2×C4×C59—22no—
377C2×C4×C59—22no—
378C2×C4×C59—22no—
379C2×C4×C59—22no—
380C2×C4×C59—22no—
381C2×C4×C59—22no—
382C2×C4×C59—41no—
383C2×C4×C59—41no—
384C2×C4×C59—41no—
385C2×C4×C59—41no—
386C2×C4×C59—41no—
387C2×C4×C59—41no—
388C2×C4×C59—41no—
389C2×C4×C59—41no—
390C2×C4×C59—41no—
391C2×C4×C59—41no—
392C2×C4×C59—41no—
393C2×C4×C59—41no—
394C2×C4×C59—41no—
395C2×C4×C59—41no—
396C2×C4×C59—41no—
397C2×C4×C59—41no—
398C2×C4×C59—41no—
399C2×C4×C59—41no—
400C2×C4×C59—41no—
401C2×C4×C59—41no—
402C2×C4×C59—41no—
403C2×C4×C59—41no—
404C2×C4×C59—41no—
405C2×C4×C59—41no—
406C2×C4×C59—41no—
407C2×C4×C59—41no—
408C2×C4×C59—41no—
409C2×C4×C59—41no—
410C2×C4×C59—41no—
411C2×C4×C59—41no—
412C22⋊D59—416no—
413C2×Dic59—22no—
414C2×Dic59—22no—
415C2×Dic59—22no—
416C2×Dic59—22no—
417C2×Dic59—22no—
418C2×Dic59—22no—
419C2×Dic59—22no—
420C2×Dic59—22no—
421C2×Dic59—22no—
422C2×Dic59—41no—
423C2×Dic59—41no—
424C2×Dic59—41no—
425C2×Dic59—41no—
426C2×Dic59—41no—
427C2×Dic59—41no—
428C2×Dic59—41no—
429C2×Dic59—41no—
430C2×Dic59—41no—
431C2×Dic59—41no—
432C2×Dic59—41no—
433C2×Dic59—41no—
434C2×Dic59—41no—
435C2×Dic59—41no—
436C2×Dic59—41no—
437C2×Dic59—41no—
438C2×Dic59—41no—
439C2×Dic59—41no—
440C2×Dic59—41no—
441C2×Dic59—41no—
442C2×Dic59—41no—
443C2×Dic59—41no—
444C2×Dic59—41no—
445C2×Dic59—41no—
446C2×Dic59—41no—
447C2×Dic59—41no—
448C2×Dic59—41no—
449C2×Dic59—41no—
450C2×Dic59—41no—
451C2×Dic59—41no—
452C2×Dic59—41no—
453C2×Dic59—41no—
454C2×Dic59—41no—
455C2×Dic59—41no—
456C2×Dic59—41no—
457C2×Dic59—41no—
458C2×Dic59—41no—
459C2×Dic59—41no—
460C2×Dic59—41no—
461C2×Dic59—41no—
462#14645—591nomaximal, Sylow
463C22×C59—42no—
464C22×C59—42no—
465C22×C59—42no—
466C22×C59—42no—
467C22×C59—42no—
468C22×C59—42no—
469C22×C59—42no—
470C22×C59—81no—
471C22×C59—81no—
472C22×C59—81no—
473C22×C59—81no—
474C22×C59—81no—
475C22×C59—81no—
476C22×C59—81no—
477C22×C59—81no—
478C22×C59C4×#4111yescharacteristic
479C22×C59#51811yescharacteristic
480C22×C59#51811yescharacteristic
481C22×C59#51811yescharacteristic
482C22×C59#51811yescharacteristic
483C22×C59#52011yescharacteristic
484C22×C59#52011yescharacteristic
485C22×C59#53811yescharacteristic
486C22×C59#53811yescharacteristic
487C22×C59#53811yescharacteristic
488C22×C59#53811yescharacteristic
489C22×C59#53811yescharacteristic
490C22×C59#53911yescharacteristic
491C22×C59#54011yescharacteristic
492C22×C59#54011yescharacteristic
493C22×C59#54011yescharacteristic
494C22×C59#54211yescharacteristic
495C22×C59#54211yescharacteristic
496C22×C59#54211yescharacteristic
497C22×C59#56011yescharacteristic
498C22×C59#56011yescharacteristic
499C22×C59#56011yescharacteristic
500C22×C59#56011yescharacteristic
501C22×C59#56011yescharacteristic
502C22×C59#56011yescharacteristic
503C22×C59#56011yescharacteristic
504C22×C59#56011yescharacteristic
505C22×C59H(3,𝔽4)11yescharacteristic
506C22×C59#56211yescharacteristic
507C22×C59#56211yescharacteristic
508C22×C59#56211yescharacteristic
509C22×C59#56211yescharacteristic
510C22×C59#56211yescharacteristic
511C22×C59#56211yescharacteristic
512C22×C59#56311yescharacteristic
513C2×D59—42no—
514C2×D59—42no—
515C2×D59—42no—
516C2×D59—42no—
517C2×D59—42no—
518C2×D59—42no—
519C2×D59—42no—
520C2×D59—81no—
521C2×D59—81no—
522C2×D59—81no—
523C2×D59—81no—
524C2×D59—81no—
525C2×D59—81no—
526C2×D59—81no—
527C2×D59—81no—
528C4×C59—42no—
529C4×C59—42no—
530C4×C59—42no—
531C4×C59—42no—
532C4×C59—81no—
533C4×C59—81no—
534Dic59—42no—
535Dic59—42no—
536Dic59—42no—
537Dic59—81no—
538Dic59—81no—
539Dic59—81no—
540Dic59—81no—
541C2×#394—591no—
542#1445—591no—
543#1443—591no—
544#1441—591no—
545#1440—591no—
546#1440—591no—
547#1439—591no—
548#1439—591no—
549#1439—591no—
550#1439—591no—
551#1438—591no—
552#1438—591no—
553#1437—591no—
554#1437D5911yescharacteristic, complemented
555#1436—591no—
556C2×C59—82no—
557C2×C59#233311yescharacteristic
558C2×C59#233511yescharacteristic
559C2×C59#233711yescharacteristic
560C2×C59#237511yescharacteristic
561C2×C59#237611yescharacteristic
562C2×C59#237711yescharacteristic
563C2×C59#237711yescharacteristic
564C2×C59#282511yescharacteristic
565C2×C59#282611yescharacteristic
566C2×C59#282811yescharacteristic
567C2×C59#282911yescharacteristic
568C2×C59#282911yescharacteristic
569C2×C59#282911yescharacteristic
570C2×C59#283211yescharacteristic
571C2×C59#283711yescharacteristic
572D59—82no—
573C23×D4—591no—
574C22×C4⋊C4—591no—
575C22×C4⋊C4—591no—
576C22×C4⋊C4—591no—
577C22×C22⋊C4—591no—
578C22×C22⋊C4—591no—
579C22×C22⋊C4—591no—
580C22×C22⋊C4—591no—
581C22×C22⋊C4—591no—
582C22×C22⋊C4—591no—
583C22×C22⋊C4—591no—
584C22×C22⋊C4—591no—
585C22×C22⋊C4—591no—
586C22×C22⋊C4C2×D5911yescharacteristic
587C22×C22⋊C4C2×D5911yescharacteristic
588C22×C22⋊C4C2×D5911yescharacteristic
589C22×C42C2×D5911yescharacteristic
590#394—598no—
591C2×#95—591no—
592C2×#95—591no—
593C2×#95—591no—
594C2×#95—591no—
595C2×#95—591no—
596C2×#95—591no—
597C2×#95—591no—
598C2×#95—591no—
599C2×#95—591no—
600C2×#95—591no—
601C2×#95—591no—
602C2×#95—591no—
603C2×#95—591no—
604C2×#95—591no—
605C2×#95—591no—
606C2×#95C2×D5911yescharacteristic
607C2×#95C2×D5911yescharacteristic
608C2×#95C2×D5911yescharacteristic
609C59#1464511yescharacteristic, complemented, Sylow
610C25—591no—
611C25C22×D5911yescharacteristic
612C22×D4—594no—
613C22×D4—2361no—
614C22×D4—2361no—
615C22×D4—2361no—
616C22×D4—2361no—
617C22×D4—2361no—
618C22×D4—2361no—
619C23×C4—591no—
620C23×C4—591no—
621C23×C4—591no—
622C23×C4—591no—
623C23×C4—591no—
624C23×C4—591no—
625C23×C4—591no—
626C23×C4C22×D5911yescharacteristic
627C23×C4C22×D5911yescharacteristic
628C23×C4C22×D5911yescharacteristic
629C23×C4C22×D5911yescharacteristic
630C23×C4C22×D5911yescharacteristic
631C23×C4C22×D5911yescharacteristic
632C2×C4⋊C4—594no—
633C2×C4⋊C4—1182no—
634C2×C4⋊C4—2361no—
635C2×C4⋊C4—2361no—
636C2×C4⋊C4—2361no—
637C2×C4⋊C4—2361no—
638C2×C4⋊C4—2361no—
639C2×C4⋊C4—2361no—
640C2×C4⋊C4—2361no—
641C2×C22⋊C4—22no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—41no—
644C2×C22⋊C4—41no—
645C2×C22⋊C4—41no—
646C2×C22⋊C4—41no—
647C2×C22⋊C4—41no—
648C2×C22⋊C4—41no—
649C2×C22⋊C4—594no—
650C2×C22⋊C4—594no—
651C2×C22⋊C4—594no—
652C2×C22⋊C4—1182no—
653C2×C22⋊C4—1182no—
654C2×C22⋊C4—2361no—
655C2×C22⋊C4—2361no—
656C2×C22⋊C4—2361no—
657C2×C22⋊C4—2361no—
658C2×C22⋊C4—2361no—
659C2×C22⋊C4—2361no—
660C2×C22⋊C4—2361no—
661C2×C22⋊C4—2361no—
662C2×C22⋊C4—2361no—
663C2×C22⋊C4—2361no—
664C2×C22⋊C4—2361no—
665C2×C22⋊C4—2361no—
666C2×C22⋊C4—2361no—
667C2×C22⋊C4—2361no—
668C2×C22⋊C4—2361no—
669C2×C22⋊C4—2361no—
670C2×C22⋊C4—2361no—
671C2×C22⋊C4—2361no—
672C2×C22⋊C4—2361no—
673C2×C22⋊C4—2361no—
674C2×C22⋊C4—2361no—
675C2×C22⋊C4—2361no—
676C2×C22⋊C4C4×D5914yes—
677C2×C42—41no—
678C2×C42—41no—
679C2×C42—41no—
680#95—41no—
681#95—41no—
682#95—41no—
683#95—594no—
684#95—1182no—
685#95—2361no—
686#95—2361no—
687#95—2361no—
688#95—2361no—
689#95—2361no—
690#95—2361no—
691#95—2361no—
692#95—2361no—
693#95—2361no—
694#95—2361no—
695#95—2361no—
696#95—2361no—
697#95—2361no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—592no—
713C24—1181no—
714C24—1181no—
715C24—1181no—
716C24—1181no—
717C24—1181no—
718C24—1181no—
719C24—1181no—
720C24—1181no—
721C24—1181no—
722C24—1181no—
723C24—1181no—
724C24—1181no—
725C24—1181no—
726C24—1181no—
727C24C2×C4×D5912yes—
728C24C23×D5911yescharacteristic
729C2×D4—2364no—
730C2×D4—2364no—
731C2×D4—2364no—
732C2×D4—2364no—
733C2×D4—2364no—
734C2×D4—2364no—
735C2×D4—2364no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—592no—
775C22×C4—592no—
776C22×C4—592no—
777C22×C4—1181no—
778C22×C4—1181no—
779C22×C4—1181no—
780C22×C4—1181no—
781C22×C4—1181no—
782C22×C4—1181no—
783C22×C4—1181no—
784C22×C4—1181no—
785C22×C4—1181no—
786C22×C4—1181no—
787C22×C4—1181no—
788C22×C4—1181no—
789C22×C4—1181no—
790C22×C4—1181no—
791C22×C4—1181no—
792C22×C4—1181no—
793C22×C4—1181no—
794C22×C4—1181no—
795C22×C4—1181no—
796C22×C4—1181no—
797C22×C4—1181no—
798C22×C4—1181no—
799C22×C4—1181no—
800C22×C4—1181no—
801C22×C4—1181no—
802C22×C4—1181no—
803C22×C4—1181no—
804C22×C4—1181no—
805C22×C4—1181no—
806C22×C4—1181no—
807C22×C4—1181no—
808C22×C4—1181no—
809C22×C4—1181no—
810C22×C4—1181no—
811C22×C4—1181no—
812C22×C4—1181no—
813C22×C4—1181no—
814C22×C4—1181no—
815C22×C4—1181no—
816C22×C4—1181no—
817C22×C4—1181no—
818C22×C4—1181no—
819C22×C4—1181no—
820C22×C4—1181no—
821C22×C4—1181no—
822C22×C4—1181no—
823C22×C4C2×C4×D5912yes—
824C22×C4C2×C4×D5912yes—
825C22×C4#1174568512yes—
826C22×C4#1174568512yes—
827C4⋊C4—2364no—
828C4⋊C4—2364no—
829C4⋊C4—2364no—
830C22⋊C4—44no—
831C22⋊C4—44no—
832C22⋊C4—44no—
833C22⋊C4—2364no—
834C22⋊C4—2364no—
835C22⋊C4—2364no—
836C22⋊C4—2364no—
837C22⋊C4—2364no—
838C22⋊C4—2364no—
839C22⋊C4—2364no—
840C22⋊C4—2364no—
841C22⋊C4—2364no—
842C42—44no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—1182no—
879C23—1182no—
880C23—1182no—
881C23—1182no—
882C23—1182no—
883C23—1182no—
884C23—1182no—
885C23—2361no—
886C23—2361no—
887C23—2361no—
888C23—2361no—
889C23—2361no—
890C23—2361no—
891C23—2361no—
892C23—2361no—
893C23—2361no—
894C23—2361no—
895C23—2361no—
896C23—2361no—
897C23—2361no—
898C23—2361no—
899C23—2361no—
900C23—2361no—
901C23—2361no—
902C23—2361no—
903C23—2361no—
904C23—2361no—
905C23—2361no—
906C23—2361no—
907C23—2361no—
908C23—2361no—
909C23—2361no—
910C23—2361no—
911C23—2361no—
912C23—2361no—
913C23C22×C4×D5911yescharacteristic
914C23C2×#1174568511yescharacteristic
915C23C2×#1174568511yescharacteristic
916C23#1427377211yescharacteristic
917C23#1427377211yescharacteristic
918C23#1427377211yescharacteristic
919C23#1427377211yescharacteristic
920C23#1427377211yescharacteristic
921C23#1427377211yescharacteristic
922C23#1427377311yescharacteristic
923C23#1427377311yescharacteristic
924C23#1427377311yescharacteristic
925C23#1427377311yescharacteristic
926C23#1427377411yescharacteristic
927C23#1427377411yescharacteristic
928D4—23616no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—1182no—
972C2×C4—1182no—
973C2×C4—1182no—
974C2×C4—1182no—
975C2×C4—1182no—
976C2×C4—1182no—
977C2×C4—1182no—
978C2×C4—1182no—
979C2×C4—1182no—
980C2×C4—2361no—
981C2×C4—2361no—
982C2×C4—2361no—
983C2×C4—2361no—
984C2×C4—2361no—
985C2×C4—2361no—
986C2×C4—2361no—
987C2×C4—2361no—
988C2×C4—2361no—
989C2×C4—2361no—
990C2×C4—2361no—
991C2×C4—2361no—
992C2×C4—2361no—
993C2×C4—2361no—
994C2×C4—2361no—
995C2×C4—2361no—
996C2×C4—2361no—
997C2×C4—2361no—
998C2×C4—2361no—
999C2×C4—2361no—
1000C2×C4—2361no—
1001C2×C4—2361no—
1002C2×C4—2361no—
1003C2×C4—2361no—
1004C2×C4—2361no—
1005C2×C4—2361no—
1006C2×C4—2361no—
1007C2×C4—2361no—
1008C2×C4—2361no—
1009C2×C4—2361no—
1010C2×C4—2361no—
1011C2×C4—2361no—
1012C2×C4—2361no—
1013C2×C4—2361no—
1014C2×C4—2361no—
1015C2×C4—2361no—
1016C2×C4—2361no—
1017C2×C4—2361no—
1018C2×C4—2361no—
1019C2×C4—2361no—
1020C22—42no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—81no—
1031C22—81no—
1032C22—81no—
1033C22—81no—
1034C22—81no—
1035C22—4721no—
1036C22—4721no—
1037C22—4721no—
1038C22—4721no—
1039C22—4721no—
1040C22—4721no—
1041C22—4721no—
1042C22—4721no—
1043C22—2362no—
1044C22—2362no—
1045C22—2362no—
1046C22—2362no—
1047C22—2362no—
1048C22—2362no—
1049C22—2362no—
1050C22C4×#1174568511yescharacteristic
1051C22#1683787411yescharacteristic
1052C22#1683787411yescharacteristic
1053C22#1683787411yescharacteristic
1054C22#1683787511yescharacteristic
1055C22#1683788111yescharacteristic
1056C22#1683788211yescharacteristic
1057C22#1683798511yescharacteristic
1058C22#1683798511yescharacteristic
1059C22#1683798511yescharacteristic
1060C22#1683799011yescharacteristic
1061C22#1683799011yescharacteristic
1062C22#1683799411yescharacteristic
1063C22#1683800311yescharacteristic
1064C22#1683800311yescharacteristic
1065C22#1683800711yescharacteristic
1066C22#1683801711yescharacteristic
1067C22#1683801711yescharacteristic
1068C22#1683802311yescharacteristic
1069C22#1683813911yescharacteristic
1070C22#1683814011yescharacteristic
1071C22#1683814011yescharacteristic
1072C22#1683814011yescharacteristic
1073C22#1683814011yescharacteristic
1074C22#1683814111yescharacteristic
1075C22#1683814211yescharacteristic
1076C22#1683814311yescharacteristic
1077C22#1683814411yescharacteristic
1078C22#1683814611yescharacteristic
1079C22#1683814611yescharacteristic
1080C22#1683814711yescharacteristic
1081C22#1683814711yescharacteristic
1082C22#1683814911yescharacteristic
1083C22#1683814911yescharacteristic
1084C22#1683815411yescharacteristic
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—81no—
1090C4—81no—
1091C4—4721no—
1092C4—4721no—
1093C4—4721no—
1094C4—4721no—
1095C4—2362no—
1096C4—2362no—
1097C4—2362no—
1098C2—82no—
1099C2—4722no—
1100C2#2142685611yescharacteristic
1101C2#2142688611yescharacteristic
1102C2#2142690411yescharacteristic
1103C2#2142723311yescharacteristic
1104C2#2142723811yescharacteristic
1105C2#2142724911yescharacteristic
1106C2#2142725411yescharacteristic
1107C2#2143218211yescharacteristic
1108C2#2143219111yescharacteristic
1109C2#2143221311yescharacteristic
1110C2#2143222211yescharacteristic
1111C2#2143222411yescharacteristic
1112C2#2143222411yescharacteristic
1113C2#2143226111yescharacteristic
1114C2#2143230811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×#1437C2
socle, cosocleC24×C59C24
prime radicalC23×C22⋊D59C22
hypercenter#1437D59
hypocenterC59#14645
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. #21422362C2semidirect
3. #21422357C2semidirect
4. #21422350C2semidirect
5. #21422344C2semidirect
6. #21422343C2semidirect
7. #21422342C2semidirect
8. #21422341C2semidirect
9. #21422340C2semidirect
10. #21422339C2semidirect
13. #21422334C2semidirect
14. #21422329C2semidirect
15. C59×#1437C2semidirect
29. #16837317C4semidirect
554. #1437D59semidirect
609. C59#14645semidirect

Maximal subgroups

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

subgroupindex
C2×#168373172
#214223622
#214223572
#214223502
#214223442
#214223432
#214223422
#214223412
#214223402
#214223392
#214223352
#214223342
#214223292
C59×#14372
#1464559