Finite Group Databasebeta

← #28510751

Subgroups — #28510751

Order 15104.

1602 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837267C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×Dic59C211yesmaximal, characteristic
3C2×C22⋊C4×Dic59C211yesmaximal, characteristic
4#21422343C211yesmaximal, characteristic
5#21422343C211yesmaximal, characteristic
6#21422341C211yesmaximal, characteristic
7#21422330C211yesmaximal, characteristic, complemented
8#21422328C211yesmaximal, characteristic, complemented
9#21422322C211yesmaximal, characteristic, complemented
10#21422322C211yesmaximal, characteristic, complemented
11#21422321C211yesmaximal, characteristic, complemented
12#21422320C211yesmaximal, characteristic, complemented
13#21422320C211yesmaximal, characteristic, complemented
14#21422318C211yesmaximal, characteristic
15C59×#1439C211yesmaximal, characteristic
16C24×Dic59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×C22⋊Dic59C2211yescharacteristic
19C22×C22⋊Dic59C2211yescharacteristic
20C22×C22⋊Dic59C2211yescharacteristic
21C22×C4×Dic59C2211yescharacteristic
22C22×C4×Dic59C2211yescharacteristic
23C22×C4×Dic59C2211yescharacteristic
24C22×C4×Dic59C2211yescharacteristic
25#16837267—24no—
26C22⋊C4×Dic59—24no—
27C22⋊C4×Dic59C418yescomplemented
28C2×C59⋊#95C2211yescharacteristic
29C2×C59⋊#95C2211yescharacteristic
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
45C2×C59⋊#95C2211yescharacteristic
46C2×C59⋊#95C2211yescharacteristic
47C22×C4⋊C4×C59C2211yescharacteristic
48C22×C22⋊C4×C59C2211yescharacteristic
49C22×C22⋊C4×C59C2211yescharacteristic
50C22×C22⋊C4×C59C2211yescharacteristic
51C2×#95×C59C2211yescharacteristic
52C2×#95×C59C2211yescharacteristic
53C2×#95×C59C2211yescharacteristic
54C23×Dic59—22no—
55C23×Dic59—22no—
56C23×Dic59—22no—
57C23×Dic59—22no—
58C23×Dic59—41no—
59C23×Dic59—41no—
60C23×Dic59C2×C414yes—
61C23×Dic59C2311yescharacteristic
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2311yescharacteristic
64C23×Dic59C2311yescharacteristic
65C23×Dic59C2311yescharacteristic
66C23×Dic59C2311yescharacteristic
67C23×Dic59C2311yescharacteristic
68C23×Dic59C2311yescharacteristic
69C2×C4⋊Dic59—22no—
70C2×C4⋊Dic59—22no—
71C2×C4⋊Dic59—41no—
72C2×C22⋊Dic59—22no—
73C2×C22⋊Dic59—22no—
74C2×C22⋊Dic59—22no—
75C2×C22⋊Dic59—22no—
76C2×C22⋊Dic59—22no—
77C2×C22⋊Dic59—22no—
78C2×C22⋊Dic59—41no—
79C2×C22⋊Dic59—41no—
80C2×C22⋊Dic59C2×C414yes—
81C2×C4×Dic59—22no—
82C2×C4×Dic59—22no—
83C2×C4×Dic59—22no—
84C2×C4×Dic59—22no—
85C2×C4×Dic59—22no—
86C2×C4×Dic59—22no—
87C2×C4×Dic59—41no—
88C2×C4×Dic59—41no—
89C2×C4×Dic59—41no—
90C2×C4×Dic59—41no—
91C2×C4×Dic59C2×C414yes—
92C2×C4×Dic59C2×C414yes—
93C59⋊#95—22no—
94C59⋊#95—22no—
95C59⋊#95—22no—
96C59⋊#95—22no—
97C59⋊#95—22no—
98C59⋊#95—22no—
99C59⋊#95—22no—
100C59⋊#95—22no—
101C59⋊#95—22no—
102C59⋊#95—22no—
103C59⋊#95—22no—
104C59⋊#95—41no—
105C59⋊#95—41no—
106C59⋊#95—41no—
107C59⋊#95—41no—
108C59⋊#95—41no—
109C59⋊#95C2×C414yes—
110C59⋊#95C2×C414yes—
111C59⋊#95D414yes—
112C25×C59C2311yescharacteristic
113C23×C4×C59C2311yescharacteristic
114C23×C4×C59C2311yescharacteristic
115C23×C4×C59C2311yescharacteristic
116C23×C4×C59C2311yescharacteristic
117C23×C4×C59C2311yescharacteristic
118C23×C4×C59C2311yescharacteristic
119C2×C4⋊C4×C59—22no—
120C2×C4⋊C4×C59—22no—
121C2×C4⋊C4×C59—41no—
122C2×C22⋊C4×C59—22no—
123C2×C22⋊C4×C59—22no—
124C2×C22⋊C4×C59—22no—
125C2×C22⋊C4×C59—22no—
126C2×C22⋊C4×C59—22no—
127C2×C22⋊C4×C59—22no—
128C2×C22⋊C4×C59—41no—
129C2×C22⋊C4×C59—41no—
130C2×C22⋊C4×C59C2×C414yes—
131#95×C59—22no—
132#95×C59—22no—
133#95×C59—41no—
134C24×C59—21no—
135C24×C59—21no—
136C24×C59—21no—
137C24×C59—21no—
138C24×C59—21no—
139C24×C59—21no—
140C24×C59—21no—
141C24×C59—21no—
142C24×C59—21no—
143C24×C59—21no—
144C24×C59—21no—
145C24×C59—21no—
146C24×C59C22×C412yes—
147C24×C59#4112yes—
148C24×C59#4112yes—
149C24×C59C2411yescharacteristic
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×C59C22×C412yes—
187C22×C4×C59C22×C412yes—
188C22×C4×C59C2×D412yes—
189C22×C4×C59#4112yes—
190C22×C4×C59#4112yes—
191C22×C4×C59#4112yes—
192C22×Dic59—21no—
193C22×Dic59—21no—
194C22×Dic59—21no—
195C22×Dic59—21no—
196C22×Dic59—21no—
197C22×Dic59—21no—
198C22×Dic59—21no—
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—28no—
225C22×Dic59—28no—
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—44no—
241C22×Dic59—44no—
242C22×Dic59—44no—
243C22×Dic59—44no—
244C22×Dic59—44no—
245C22×Dic59C22×C412yes—
246C22×Dic59C22×C412yes—
247C22×Dic59C22×C412yes—
248C22×Dic59C22×C412yes—
249C22×Dic59C2×D412yes—
250C22×Dic59C2×D412yes—
251C22×Dic59#4112yes—
252C22×Dic59#4112yes—
253C22×Dic59#4112yes—
254C22×Dic59#4112yes—
255C4⋊C4×C59—44no—
256C22⋊C4×C59—28no—
257C22⋊C4×C59—28no—
258C22⋊C4×C59—44no—
259C22⋊Dic59—28no—
260C22⋊Dic59—28no—
261C22⋊Dic59—44no—
262C4⋊Dic59—44no—
263C4×Dic59—28no—
264C4×Dic59—44no—
265C4×Dic59—44no—
266C4×Dic59—44no—
267C23×C59—22no—
268C23×C59—22no—
269C23×C59—22no—
270C23×C59—22no—
271C23×C59—22no—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59—22no—
275C23×C59—22no—
276C23×C59—22no—
277C23×C59—22no—
278C23×C59—22no—
279C23×C59—22no—
280C23×C59—22no—
281C23×C59—22no—
282C23×C59—22no—
283C23×C59—22no—
284C23×C59—22no—
285C23×C59—41no—
286C23×C59—41no—
287C23×C59—41no—
288C23×C59—41no—
289C23×C59—41no—
290C23×C59—41no—
291C23×C59—41no—
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#11714yes—
302C23×C59C23×C411yescharacteristic
303C23×C59C22×D411yescharacteristic
304C23×C59C2×#4111yescharacteristic
305C23×C59C2×#4111yescharacteristic
306C23×C59C2×#4111yescharacteristic
307C23×C59C2×#4111yescharacteristic
308C23×C59C2×#4111yescharacteristic
309C23×C59C2×#4111yescharacteristic
310C23×C59C2×#4111yescharacteristic
311C23×C59C2×#4111yescharacteristic
312C23×C59C2×#4111yescharacteristic
313C23×C59H(5,𝔽2)11yescharacteristic
314C23×C59H(5,𝔽2)11yescharacteristic
315C23×C59H(5,𝔽2)11yescharacteristic
316C23×C592−1+411yescharacteristic
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—22no—
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#11714yes—
359C2×Dic59—22no—
360C2×Dic59—22no—
361C2×Dic59—22no—
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—22no—
381C2×Dic59—22no—
382C2×Dic59—22no—
383C2×Dic59—416no—
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—41no—
411C2×Dic59—41no—
412C2×Dic59—41no—
413C2×Dic59—41no—
414C2×Dic59#11714yes—
415C2×Dic59C4×D414yes—
416#13888—591nomaximal, Sylow
417C22×C59—24no—
418C22×C59—24no—
419C22×C59—24no—
420C22×C59—42no—
421C22×C59—42no—
422C22×C59—42no—
423C22×C59—42no—
424C22×C59—42no—
425C22×C59—42no—
426C22×C59—42no—
427C22×C59—42no—
428C22×C59—42no—
429C22×C59—42no—
430C22×C59—42no—
431C22×C59—42no—
432C22×C59C2×#11711yescharacteristic
433C22×C59C2×#11711yescharacteristic
434C22×C59C2×#11711yescharacteristic
435C22×C59C2×C4×D411yescharacteristic
436C22×C59C4×#4111yescharacteristic
437C22×C59#51811yescharacteristic
438C22×C59#52011yescharacteristic
439C22×C59#52511yescharacteristic
440C22×C59#52511yescharacteristic
441C22×C59#52911yescharacteristic
442C22×C59#52911yescharacteristic
443C22×C59#52911yescharacteristic
444C22×C59#52911yescharacteristic
445C22×C59#52911yescharacteristic
446C22×C59#52911yescharacteristic
447C22×C59#53811yescharacteristic
448C22×C59#53811yescharacteristic
449C22×C59#53911yescharacteristic
450C22×C59#53911yescharacteristic
451C22×C59#54611yescharacteristic
452C22×C59#54611yescharacteristic
453C22×C59#54611yescharacteristic
454C22×C59#54811yescharacteristic
455C22×C59#55111yescharacteristic
456C22×C59#55111yescharacteristic
457C22×C59#55211yescharacteristic
458C22×C59#55211yescharacteristic
459C22×C59#55211yescharacteristic
460C22×C59#55311yescharacteristic
461C22×C59#55311yescharacteristic
462C22×C59#55311yescharacteristic
463C22×C59#55511yescharacteristic
464C22×C59#55511yescharacteristic
465C22×C59#55911yescharacteristic
466C22×C59#55911yescharacteristic
467C4×C59—24no—
468C4×C59—42no—
469C4×C59—42no—
470C4×C59—42no—
471C4×C59—81no—
472C4×C59—81no—
473Dic59—24no—
474Dic59—24no—
475Dic59—42no—
476Dic59—42no—
477Dic59—42no—
478Dic59—42no—
479Dic59—81no—
480Dic59—81no—
481C2×#382—591no—
482C2×C4×C22⋊C4—591no—
483C2×C4×C22⋊C4—591no—
484#1440—591no—
485#1440—591no—
486#1439—591no—
487#1439D5911yescharacteristic
488#1436—591no—
489#1436—591no—
490#1434—591no—
491#1434—591no—
492#1434—591no—
493#1434—591no—
494#1434—591no—
495C22⋊#95—591no—
496C2×C59—44no—
497C2×C59#228311yescharacteristic
498C2×C59#229011yescharacteristic
499C2×C59#231811yescharacteristic
500C2×C59#234211yescharacteristic
501C2×C59#234611yescharacteristic
502C2×C59#235211yescharacteristic
503C2×C59#235711yescharacteristic
504C2×C59#245911yescharacteristic
505C2×C59#245911yescharacteristic
506C2×C59#246011yescharacteristic
507C2×C59#246011yescharacteristic
508C2×C59#251711yescharacteristic
509C2×C59#251711yescharacteristic
510C2×C59#251811yescharacteristic
511C2×C59#251811yescharacteristic
512C24×C4—591no—
513C22×C4⋊C4—591no—
514C22×C4⋊C4C2×D5911yescharacteristic
515C22×C22⋊C4—591no—
516C22×C22⋊C4—591no—
517C22×C22⋊C4—591no—
518C22×C22⋊C4C2×D5911yescharacteristic
519C22×C22⋊C4C2×D5911yescharacteristic
520C22×C22⋊C4C2×D5911yescharacteristic
521C22×C42—591no—
522C22×C42—591no—
523C22×C42—591no—
524C22×C42—591no—
525#382—1184no—
526C4×C22⋊C4—598no—
527C4×C22⋊C4—1184no—
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×#95—591no—
540C2×#95—591no—
541C2×#95—591no—
542C2×#95—591no—
543C2×#95—591no—
544C2×#95—591no—
545C2×#95—591no—
546C2×#95—591no—
547C2×#95C2×D5911yescharacteristic
548C2×#95C2×D5911yescharacteristic
549C2×#95C2×D5911yescharacteristic
550C59#1388811yescharacteristic, complemented, Sylow
551C25C22×D5911yescharacteristic
552C23×C4—591no—
553C23×C4—591no—
554C23×C4—591no—
555C23×C4—591no—
556C23×C4—591no—
557C23×C4—591no—
558C23×C4—594no—
559C23×C4—591no—
560C23×C4—591no—
561C23×C4—1182no—
562C23×C4—1182no—
563C23×C4—1182no—
564C23×C4—1182no—
565C23×C4—2361no—
566C23×C4—2361no—
567C23×C4C22×D5911yescharacteristic
568C23×C4C22×D5911yescharacteristic
569C23×C4C22×D5911yescharacteristic
570C23×C4C22×D5911yescharacteristic
571C23×C4C22×D5911yescharacteristic
572C23×C4C22×D5911yescharacteristic
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—41no—
576C2×C4⋊C4—1182no—
577C2×C4⋊C4—1182no—
578C2×C4⋊C4—2361no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—594no—
588C2×C22⋊C4—1182no—
589C2×C22⋊C4—1182no—
590C2×C22⋊C4—1182no—
591C2×C22⋊C4—1182no—
592C2×C22⋊C4—1182no—
593C2×C22⋊C4—1182no—
594C2×C22⋊C4—2361no—
595C2×C22⋊C4—2361no—
596C2×C22⋊C4C4×D5914yes—
597C2×C42—594no—
598C2×C42—594no—
599C2×C42—1182no—
600C2×C42—1182no—
601C2×C42—1182no—
602C2×C42—1182no—
603C2×C42—1182no—
604C2×C42—1182no—
605C2×C42—2361no—
606C2×C42—2361no—
607C2×C42—2361no—
608C2×C42—2361no—
609#95—22no—
610#95—22no—
611#95—41no—
612#95—594no—
613#95—594no—
614#95—594no—
615#95—1182no—
616#95—1182no—
617#95—1182no—
618#95—1182no—
619#95—1182no—
620#95—1182no—
621#95—1182no—
622#95—1182no—
623#95—1182no—
624#95—1182no—
625#95—1182no—
626#95—2361no—
627#95—2361no—
628#95—2361no—
629#95—2361no—
630#95—2361no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24C2×C4×D5912yes—
644C24#1174568712yes—
645C24#1174568912yes—
646C24C23×D5911yescharacteristic
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—592no—
684C22×C4—592no—
685C22×C4—592no—
686C22×C4—592no—
687C22×C4—592no—
688C22×C4—592no—
689C22×C4—592no—
690C22×C4—592no—
691C22×C4—592no—
692C22×C4—592no—
693C22×C4—1188no—
694C22×C4—1188no—
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×C4—1181no—
734C22×C4—1181no—
735C22×C4—1181no—
736C22×C4—1181no—
737C22×C4—1181no—
738C22×C4—1181no—
739C22×C4—1181no—
740C22×C4—1181no—
741C22×C4—2364no—
742C22×C4—2364no—
743C22×C4—2364no—
744C22×C4—2364no—
745C22×C4—2364no—
746C22×C4C2×C4×D5912yes—
747C22×C4C2×C4×D5912yes—
748C22×C4D4×D5912yes—
749C22×C4#1174568712yes—
750C22×C4#1174568712yes—
751C22×C4#1174568712yes—
752C4⋊C4—44no—
753C4⋊C4—2364no—
754C22⋊C4—28no—
755C22⋊C4—28no—
756C22⋊C4—44no—
757C22⋊C4—1188no—
758C22⋊C4—1188no—
759C22⋊C4—2364no—
760C42—1188no—
761C42—2364no—
762C42—2364no—
763C42—2364no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23#1427368514yes—
799C23C22×C4×D5911yescharacteristic
800C23C2×D4×D5911yescharacteristic
801C23#41×D5911yescharacteristic
802C23#41×D5911yescharacteristic
803C23#41×D5911yescharacteristic
804C23#41×D5911yescharacteristic
805C23C2×#1174568711yescharacteristic
806C23C2×#1174568711yescharacteristic
807C23C2×#1174568711yescharacteristic
808C23C2×#1174568711yescharacteristic
809C23C2×#1174568911yescharacteristic
810C23#1427377211yescharacteristic
811C23#1427377211yescharacteristic
812C23#1427377311yescharacteristic
813C23#1427377411yescharacteristic
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—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
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—41no—
854C2×C4—41no—
855C2×C4—594no—
856C2×C4—594no—
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—1182no—
873C2×C4—1182no—
874C2×C4—1182no—
875C2×C4—1182no—
876C2×C4—1182no—
877C2×C4—1182no—
878C2×C4—1182no—
879C2×C4—1182no—
880C2×C4—1182no—
881C2×C4—23616no—
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—2361no—
903C2×C4—2361no—
904C2×C4—2361no—
905C2×C4—2361no—
906C2×C4—2361no—
907C2×C4—2361no—
908C2×C4—2361no—
909C2×C4—2361no—
910C2×C4—2361no—
911C2×C4—2361no—
912C2×C4#1427368314yes—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22#117×D5911yescharacteristic
929C22C2×#1427368311yescharacteristic
930C22C2×#1427368511yescharacteristic
931C22C4×D4×D5911yescharacteristic
932C22C4×#1174568711yescharacteristic
933C22#1683787411yescharacteristic
934C22#1683788111yescharacteristic
935C22#1683790811yescharacteristic
936C22#1683791511yescharacteristic
937C22#1683792911yescharacteristic
938C22#1683793311yescharacteristic
939C22#1683793311yescharacteristic
940C22#1683793811yescharacteristic
941C22#1683793811yescharacteristic
942C22#1683793811yescharacteristic
943C22#1683798711yescharacteristic
944C22#1683799211yescharacteristic
945C22#1683799611yescharacteristic
946C22#1683800111yescharacteristic
947C22#1683803911yescharacteristic
948C22#1683804111yescharacteristic
949C22#1683804511yescharacteristic
950C22#1683805811yescharacteristic
951C22#1683807711yescharacteristic
952C22#1683808011yescharacteristic
953C22#1683808811yescharacteristic
954C22#1683808911yescharacteristic
955C22#1683808911yescharacteristic
956C22#1683809511yescharacteristic
957C22#1683809911yescharacteristic
958C22#1683810411yescharacteristic
959C22#1683811411yescharacteristic
960C22#1683811611yescharacteristic
961C22#1683813411yescharacteristic
962C22#1683813811yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—81no—
968C4—81no—
969C4—1184no—
970C4—1184no—
971C4—4721no—
972C4—4721no—
973C4—2362no—
974C4—2362no—
975C4—2362no—
976C4—2362no—
977C2—44no—
978C2#2142649111yescharacteristic
979C2#2142653211yescharacteristic
980C2#2142672411yescharacteristic
981C2#2142694411yescharacteristic
982C2#2142697811yescharacteristic
983C2#2142702311yescharacteristic
984C2#2142706811yescharacteristic
985C2#2142802811yescharacteristic
986C2#2142803611yescharacteristic
987C2#2142804311yescharacteristic
988C2#2142805111yescharacteristic
989C2#2142874011yescharacteristic
990C2#2142874511yescharacteristic
991C2#2142874911yescharacteristic
992C2#2142875711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×#1439C2
socle, cosocleC24×C59C24
prime radicalC25×C59C23
hypercenter#1439D59
hypocenterC59#13888
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×#16837267C2semidirect
7. #21422330C2semidirect
8. #21422328C2semidirect
9. #21422322C2semidirect
10. #21422322C2semidirect
11. #21422321C2semidirect
12. #21422320C2semidirect
13. #21422320C2semidirect
27. C22⋊C4×Dic59C4semidirect
550. C59#13888semidirect

Maximal subgroups

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

subgroupindex
C2×#168372672
C2×C22⋊C4×Dic592
#214223432
#214223412
#214223302
#214223282
#214223222
#214223212
#214223202
#214223182
C59×#14392
#1388859