Finite Group Databasebeta

← #28517260

Subgroups — #28517260

Order 15104.

1450 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837275C211yesmaximal, characteristic
2#21422362C211yesmaximal, characteristic, complemented
3#21422357C211yesmaximal, characteristic, complemented
4#21422347C211yesmaximal, characteristic, complemented
5#21422347C211yesmaximal, characteristic, complemented
6#21422339C211yesmaximal, characteristic
7#21422339C211yesmaximal, characteristic
8#21422333C211yesmaximal, characteristic
9#21422333C211yesmaximal, characteristic
10#21422327C211yesmaximal, characteristic, complemented
11Dic59⋊#95C211yesmaximal, characteristic, complemented
12#21422322C211yesmaximal, characteristic, complemented
13#21422322C211yesmaximal, characteristic, complemented
14#21422319C211yesmaximal, characteristic
15C59×C22⋊#95C211yesmaximal, characteristic
16C22×Dic59⋊C4C2211yescharacteristic
17C22×Dic59⋊C4C2211yescharacteristic
18C22×Dic59⋊C4C2211yescharacteristic
19C22×Dic59⋊C4C2211yescharacteristic
20C22×C22⋊Dic59C2211yescharacteristic
21C22×C22⋊Dic59C2211yescharacteristic
22C22×C22⋊Dic59C2211yescharacteristic
23C22×C22⋊Dic59C2211yescharacteristic
24C22×C4×Dic59C2211yescharacteristic
25C22×C4×Dic59C2211yescharacteristic
26#16837275C418yescomplemented
27C2×C59⋊#95C2211yescharacteristic
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
45C24×C4×C59C2211yescharacteristic
46C22×C22⋊C4×C59C2211yescharacteristic
47C22×C22⋊C4×C59C2211yescharacteristic
48C2×#95×C59C2211yescharacteristic
49C2×#95×C59C2211yescharacteristic
50C2×#95×C59C2211yescharacteristic
51C2×#95×C59C2211yescharacteristic
52C23×Dic59C2311yescharacteristic
53C23×Dic59C2311yescharacteristic
54C23×Dic59C2311yescharacteristic
55C23×Dic59C2311yescharacteristic
56C23×Dic59C2311yescharacteristic
57C23×Dic59C2311yescharacteristic
58C23×Dic59C2311yescharacteristic
59C23×Dic59C2311yescharacteristic
60C2×Dic59⋊C4—22no—
61C2×Dic59⋊C4—22no—
62C2×Dic59⋊C4—41no—
63C2×Dic59⋊C4—41no—
64C2×Dic59⋊C4—41no—
65C2×Dic59⋊C4—41no—
66C2×Dic59⋊C4—41no—
67C2×Dic59⋊C4—41no—
68C2×Dic59⋊C4—41no—
69C2×Dic59⋊C4—41no—
70C2×Dic59⋊C4C2×C414yes—
71C2×Dic59⋊C4C2×C414yes—
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⋊Dic59—41no—
81C2×C22⋊Dic59—41no—
82C2×C22⋊Dic59C2×C414yes—
83C2×C22⋊Dic59C2×C414yes—
84C2×C4×Dic59—22no—
85C2×C4×Dic59—22no—
86C2×C4×Dic59—22no—
87C2×C4×Dic59—41no—
88C2×C4×Dic59—41no—
89C2×C4×Dic59—41no—
90C59⋊#95—22no—
91C59⋊#95—22no—
92C59⋊#95—22no—
93C59⋊#95—41no—
94C59⋊#95—41no—
95C59⋊#95—41no—
96C59⋊#95—41no—
97C59⋊#95—41no—
98C59⋊#95—41no—
99C59⋊#95—41no—
100C59⋊#95—41no—
101C59⋊#95—41no—
102C59⋊#95—41no—
103C59⋊#95—41no—
104C59⋊#95—41no—
105C59⋊#95—41no—
106C59⋊#95C2×C414yes—
107C59⋊#95C2×C414yes—
108C25×C59C2311yescharacteristic
109C23×C4×C59—41no—
110C23×C4×C59—41no—
111C23×C4×C59—41no—
112C23×C4×C59—41no—
113C23×C4×C59—41no—
114C23×C4×C59—41no—
115C23×C4×C59C2×C414yes—
116C23×C4×C59C2311yescharacteristic
117C23×C4×C59C2311yescharacteristic
118C23×C4×C59C2311yescharacteristic
119C23×C4×C59C2311yescharacteristic
120C23×C4×C59C2311yescharacteristic
121C23×C4×C59C2311yescharacteristic
122C2×C22⋊C4×C59—22no—
123C2×C22⋊C4×C59—41no—
124C2×C22⋊C4×C59—41no—
125C2×C22⋊C4×C59—41no—
126C2×C22⋊C4×C59—41no—
127C2×C22⋊C4×C59Q814yes—
128#95×C59—41no—
129#95×C59—41no—
130#95×C59—41no—
131#95×C59—41no—
132C24×C59—21no—
133C24×C59—21no—
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×C59C22×C412yes—
145C24×C59C2×Q812yes—
146C24×C59#4112yes—
147C24×C59C2411yescharacteristic
148C22×C4×C59—21no—
149C22×C4×C59—21no—
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—44no—
187C22×C4×C59—44no—
188C22×C4×C59—44no—
189C22×C4×C59—44no—
190C22×C4×C59—44no—
191C22×C4×C59—44no—
192C22×C4×C59—44no—
193C22×C4×C59C22×C412yes—
194C22×C4×C59C22×C412yes—
195C22×C4×C59C2×Q812yes—
196C22×C4×C59C2×Q812yes—
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—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×Dic59C22×C412yes—
246C22×Dic59C22×C412yes—
247C22×Dic59C22×C412yes—
248C22×Dic59C22×C412yes—
249C22×Dic59#4112yes—
250C22×Dic59#4112yes—
251C22×Dic59#4112yes—
252C22×Dic59#4112yes—
253C22⋊C4×C59—44no—
254C22⋊C4×C59—44no—
255C22⋊Dic59—28no—
256C22⋊Dic59—44no—
257C22⋊Dic59—44no—
258C22⋊Dic59—44no—
259Dic59⋊C4—44no—
260Dic59⋊C4—44no—
261Dic59⋊C4—44no—
262Dic59⋊C4—44no—
263C4×Dic59—44no—
264C4×Dic59—44no—
265C23×C59—22no—
266C23×C59—22no—
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—41no—
284C23×C59—41no—
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×C59C4×Q814yes—
300C23×C59C23×C411yescharacteristic
301C23×C59C22×Q811yescharacteristic
302C23×C59C2×#4111yescharacteristic
303C23×C59C2×#4111yescharacteristic
304C23×C59C2×#4111yescharacteristic
305C23×C59C2×#4111yescharacteristic
306C23×C59C2×#4111yescharacteristic
307C23×C59H(5,𝔽2)11yescharacteristic
308C23×C59H(5,𝔽2)11yescharacteristic
309C23×C59H(5,𝔽2)11yescharacteristic
310C23×C59H(5,𝔽2)11yescharacteristic
311C23×C59H(5,𝔽2)11yescharacteristic
312C23×C59H(5,𝔽2)11yescharacteristic
313C23×C59H(5,𝔽2)11yescharacteristic
314C23×C592−1+411yescharacteristic
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—416no—
328C2×C4×C59—41no—
329C2×C4×C59—41no—
330C2×C4×C59—41no—
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×Dic59—22no—
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—41no—
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—41no—
411C2×Dic59—41no—
412C2×Dic59—41no—
413C2×Dic59#11714yes—
414#14456—591nomaximal, Sylow
415C22×C59—24no—
416C22×C59—24no—
417C22×C59—24no—
418C22×C59—42no—
419C22×C59—42no—
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×C59C2×#11711yescharacteristic
431C22×C59C2×C4×Q811yescharacteristic
432C22×C59C4×#4111yescharacteristic
433C22×C59#51811yescharacteristic
434C22×C59#51811yescharacteristic
435C22×C59#51811yescharacteristic
436C22×C59#52011yescharacteristic
437C22×C59#53811yescharacteristic
438C22×C59#53811yescharacteristic
439C22×C59#53911yescharacteristic
440C22×C59#53911yescharacteristic
441C22×C59#54011yescharacteristic
442C22×C59#54011yescharacteristic
443C22×C59#54011yescharacteristic
444C22×C59#54211yescharacteristic
445C22×C59#54211yescharacteristic
446C22×C59#54211yescharacteristic
447C22×C59#54311yescharacteristic
448C22×C59#54411yescharacteristic
449C22×C59#55111yescharacteristic
450C22×C59#55111yescharacteristic
451C22×C59#55111yescharacteristic
452C22×C59#55111yescharacteristic
453C22×C59#55311yescharacteristic
454C22×C59#55311yescharacteristic
455C22×C59#55311yescharacteristic
456C22×C59#55311yescharacteristic
457C22×C59#55411yescharacteristic
458C22×C59#55411yescharacteristic
459C22×C59#55411yescharacteristic
460C22×C59#55411yescharacteristic
461C22×C59#56011yescharacteristic
462C22×C59#56011yescharacteristic
463C22×C59#56011yescharacteristic
464C22×C59H(3,𝔽4)11yescharacteristic
465C4×C59—42no—
466C4×C59—42no—
467C4×C59—42no—
468C4×C59—42no—
469C4×C59—81no—
470C4×C59—81no—
471Dic59—24no—
472Dic59—42no—
473Dic59—42no—
474Dic59—42no—
475Dic59—42no—
476Dic59—42no—
477Dic59—81no—
478Dic59—81no—
479C2×#385—591no—
480#1445—591no—
481#1443—591no—
482#1441—591no—
483#1441—591no—
484#1439—591no—
485#1439—591no—
486#1437—591no—
487#1437—591no—
488#1436—591no—
489C4⋊#95—591no—
490#1434—591no—
491#1434—591no—
492C22⋊#95—591no—
493C22⋊#95D5911yescharacteristic
494C2×C59—44no—
495C2×C59#231911yescharacteristic
496C2×C59#232911yescharacteristic
497C2×C59#233511yescharacteristic
498C2×C59#234511yescharacteristic
499C2×C59#235311yescharacteristic
500C2×C59#236811yescharacteristic
501C2×C59#237511yescharacteristic
502C2×C59#274611yescharacteristic
503C2×C59#274811yescharacteristic
504C2×C59#274911yescharacteristic
505C2×C59#275311yescharacteristic
506C2×C59#275711yescharacteristic
507C2×C59#276311yescharacteristic
508C2×C59#278011yescharacteristic
509C2×C59#279011yescharacteristic
510C24×C4C2×D5911yescharacteristic
511C22×C4⋊C4—591no—
512C22×C4⋊C4—591no—
513C22×C4⋊C4—591no—
514C22×C4⋊C4—591no—
515C22×C22⋊C4—591no—
516C22×C22⋊C4—591no—
517C22×C22⋊C4—591no—
518C22×C22⋊C4—591no—
519C22×C22⋊C4C2×D5911yescharacteristic
520C22×C22⋊C4C2×D5911yescharacteristic
521C22×C42—591no—
522C22×C42—591no—
523#385—598no—
524C2×#95—591no—
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×#95—591no—
540C2×#95—591no—
541C2×#95—591no—
542C2×#95C2×D5911yescharacteristic
543C2×#95C2×D5911yescharacteristic
544C2×#95C2×D5911yescharacteristic
545C2×#95C2×D5911yescharacteristic
546C59#1445611yescharacteristic, complemented, Sylow
547C25C22×D5911yescharacteristic
548C23×C4—41no—
549C23×C4—41no—
550C23×C4—41no—
551C23×C4—41no—
552C23×C4—41no—
553C23×C4—41no—
554C23×C4—591no—
555C23×C4—591no—
556C23×C4—591no—
557C23×C4—591no—
558C23×C4—591no—
559C23×C4—591no—
560C23×C4—591no—
561C23×C4—591no—
562C23×C4C4×D5914yes—
563C23×C4C22×D5911yescharacteristic
564C23×C4C22×D5911yescharacteristic
565C23×C4C22×D5911yescharacteristic
566C23×C4C22×D5911yescharacteristic
567C23×C4C22×D5911yescharacteristic
568C23×C4C22×D5911yescharacteristic
569C2×C4⋊C4—594no—
570C2×C4⋊C4—594no—
571C2×C4⋊C4—1182no—
572C2×C4⋊C4—1182no—
573C2×C4⋊C4—2361no—
574C2×C4⋊C4—2361no—
575C2×C4⋊C4—2361no—
576C2×C4⋊C4—2361no—
577C2×C4⋊C4—2361no—
578C2×C4⋊C4—2361no—
579C2×C4⋊C4—2361no—
580C2×C4⋊C4—2361no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—41no—
583C2×C22⋊C4—41no—
584C2×C22⋊C4—41no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—594no—
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⋊C4—2361no—
597C2×C22⋊C4—2361no—
598C2×C22⋊C4Dic11814yes—
599C2×C42—1182no—
600C2×C42—1182no—
601C2×C42—1182no—
602C2×C42—2361no—
603C2×C42—2361no—
604C2×C42—2361no—
605#95—41no—
606#95—41no—
607#95—41no—
608#95—41no—
609#95—594no—
610#95—594no—
611#95—1182no—
612#95—1182no—
613#95—1182no—
614#95—2361no—
615#95—2361no—
616#95—2361no—
617#95—2361no—
618#95—2361no—
619#95—2361no—
620#95—2361no—
621#95—2361no—
622#95—2361no—
623#95—2361no—
624#95—2361no—
625#95—2361no—
626#95—2361no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24C2×Dic11812yes—
640C24C2×C4×D5912yes—
641C24#1174568512yes—
642C24C23×D5911yescharacteristic
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—44no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—592no—
689C22×C4—592no—
690C22×C4—592no—
691C22×C4—592no—
692C22×C4—592no—
693C22×C4—592no—
694C22×C4—592no—
695C22×C4—592no—
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—1181no—
742C22×C4—1181no—
743C22×C4—1181no—
744C22×C4C2×Dic11812yes—
745C22×C4C2×Dic11812yes—
746C22×C4C2×C4×D5912yes—
747C22×C4C2×C4×D5912yes—
748C4⋊C4—2364no—
749C4⋊C4—2364no—
750C4⋊C4—2364no—
751C4⋊C4—2364no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—1188no—
755C22⋊C4—2364no—
756C22⋊C4—2364no—
757C22⋊C4—2364no—
758C42—2364no—
759C42—2364no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
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—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23C4×Dic11814yes—
795C23C22×C4×D5911yescharacteristic
796C23C22×Dic11811yescharacteristic
797C23#41×D5911yescharacteristic
798C23#41×D5911yescharacteristic
799C23#41×D5911yescharacteristic
800C23#41×D5911yescharacteristic
801C23C2×#1174568511yescharacteristic
802C23#1427377211yescharacteristic
803C23#1427377211yescharacteristic
804C23#1427377211yescharacteristic
805C23#1427377211yescharacteristic
806C23#1427377211yescharacteristic
807C23#1427377211yescharacteristic
808C23#1427377211yescharacteristic
809C23#1427377511yescharacteristic
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—416no—
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—1182no—
873C2×C4—1182no—
874C2×C4—1182no—
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—2361no—
903C2×C4—2361no—
904C2×C4—2361no—
905C2×C4—2361no—
906C2×C4—2361no—
907C2×C4—2361no—
908C2×C4—2361no—
909C22—24no—
910C22—24no—
911C22—24no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22#117×D5911yescharacteristic
925C22C2×C4×Dic11811yescharacteristic
926C22#1683787011yescharacteristic
927C22#1683787511yescharacteristic
928C22#1683787511yescharacteristic
929C22#1683787511yescharacteristic
930C22#1683788311yescharacteristic
931C22#1683798411yescharacteristic
932C22#1683799011yescharacteristic
933C22#1683799811yescharacteristic
934C22#1683799911yescharacteristic
935C22#1683800211yescharacteristic
936C22#1683800211yescharacteristic
937C22#1683800211yescharacteristic
938C22#1683802211yescharacteristic
939C22#1683802211yescharacteristic
940C22#1683802211yescharacteristic
941C22#1683802811yescharacteristic
942C22#1683803311yescharacteristic
943C22#1683808011yescharacteristic
944C22#1683808011yescharacteristic
945C22#1683808111yescharacteristic
946C22#1683808111yescharacteristic
947C22#1683809711yescharacteristic
948C22#1683809711yescharacteristic
949C22#1683810111yescharacteristic
950C22#1683810111yescharacteristic
951C22#1683811111yescharacteristic
952C22#1683811111yescharacteristic
953C22#1683811111yescharacteristic
954C22#1683811111yescharacteristic
955C22#1683814111yescharacteristic
956C22#1683814111yescharacteristic
957C22#1683814111yescharacteristic
958C22#1683814511yescharacteristic
959C4—42no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—81no—
964C4—81no—
965C4—1184no—
966C4—4721no—
967C4—4721no—
968C4—2362no—
969C4—2362no—
970C4—2362no—
971C4—2362no—
972C4—2362no—
973C2—44no—
974C2#2142673811yescharacteristic
975C2#2142682911yescharacteristic
976C2#2142688211yescharacteristic
977C2#2142697411yescharacteristic
978C2#2142703311yescharacteristic
979C2#2142717911yescharacteristic
980C2#2142723511yescharacteristic
981C2#2143127711yescharacteristic
982C2#2143130711yescharacteristic
983C2#2143132211yescharacteristic
984C2#2143137611yescharacteristic
985C2#2143143611yescharacteristic
986C2#2143151011yescharacteristic
987C2#2143174111yescharacteristic
988C2#2143186911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×C22⋊#95C2
socle, cosocleC24×C59C24
prime radicalC25×C59C23
hypercenterC22⋊#95D59
hypocenterC59#14456
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. #21422362C2semidirect
3. #21422357C2semidirect
4. #21422347C2semidirect
5. #21422347C2semidirect
10. #21422327C2semidirect
11. Dic59⋊#95C2semidirect
12. #21422322C2semidirect
13. #21422322C2semidirect
26. #16837275C4semidirect
546. C59#14456semidirect

Maximal subgroups

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

subgroupindex
C2×#168372752
#214223622
#214223572
#214223472
#214223392
#214223332
#214223272
Dic59⋊#952
#214223222
#214223192
C59×C22⋊#952
#1445659