Finite Group Databasebeta

← #28516039

Subgroups — #28516039

Order 15104.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273705C211yesmaximal, characteristic
2C2×#16837306C211yesmaximal, characteristic, complemented
3C2×#16837297C211yesmaximal, characteristic, complemented
4C2×#16837289C211yesmaximal, characteristic, complemented
5C2×#16837259C211yesmaximal, characteristic
6#21422366C211yesmaximal, characteristic, complemented
7#21422349C211yesmaximal, characteristic, complemented
8#21422347C211yesmaximal, characteristic, complemented
9#21422340C211yesmaximal, characteristic
10#21422340C211yesmaximal, characteristic
11#21422332C211yesmaximal, characteristic
12#21422332C211yesmaximal, characteristic
13#21422327C211yesmaximal, characteristic, complemented
14(C2×D59)⋊#95C211yesmaximal, characteristic
15C59×#1441C211yesmaximal, characteristic, complemented
16C23×Dic118C2211yescharacteristic
17C23×C4×D59C2211yescharacteristic
18C2×#14273705—24no—
19C2×#14273705—24no—
20C2×#14273705C418yescomplemented
21C22×C4⋊Dic59C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×Dic59⋊C4C2211yescharacteristic
24C22×Dic59⋊C4C2211yescharacteristic
25C22×Dic59⋊C4C2211yescharacteristic
26C22×(C2×D59)⋊C4C2211yescharacteristic
27C22×(C2×D59)⋊C4C2211yescharacteristic
28C22×(C2×D59)⋊C4C2211yescharacteristic
29C22×(C2×D59)⋊C4C2211yescharacteristic
30C22×(C2×D59)⋊C4C2211yescharacteristic
31C22×(C2×D59)⋊C4C2211yescharacteristic
32C22×C4×Dic59C2211yescharacteristic
33C22×C4×Dic59C2211yescharacteristic
34#16837306—24no—
35#16837297—24no—
36#16837289—24no—
37#16837259—24no—
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
47C2×C59⋊#95C2211yescharacteristic
48C2×C59⋊#95C2211yescharacteristic
49C2×C59⋊#95C2211yescharacteristic
50C2×C59⋊#95C2211yescharacteristic
51C22×C4⋊C4×C59C2211yescharacteristic
52C22×C4⋊C4×C59C2211yescharacteristic
53C2×#95×C59C2211yescharacteristic
54C2×#95×C59C2211yescharacteristic
55C2×#95×C59C2211yescharacteristic
56C2×#95×C59C2211yescharacteristic
57C2×#95×C59C2211yescharacteristic
58C24×D59C2311yescharacteristic
59C22×Dic118—22no—
60C22×Dic118—22no—
61C22×Dic118—22no—
62C22×Dic118—22no—
63C22×Dic118—41no—
64C22×Dic118—41no—
65C22×Dic118C2×C414yes—
66C23×Dic59C2311yescharacteristic
67C23×Dic59C2311yescharacteristic
68C23×Dic59C2311yescharacteristic
69C23×Dic59C2311yescharacteristic
70C23×Dic59C2311yescharacteristic
71C23×Dic59C2311yescharacteristic
72C23×Dic59C2311yescharacteristic
73C22×C4×D59—22no—
74C22×C4×D59—22no—
75C22×C4×D59—22no—
76C22×C4×D59—22no—
77C22×C4×D59—41no—
78C22×C4×D59—41no—
79C22×C4×D59C2×C414yes—
80#14273705—232no—
81C2×C4⋊Dic59—22no—
82C2×C4⋊Dic59—22no—
83C2×C4⋊Dic59—41no—
84C2×Dic59⋊C4—22no—
85C2×Dic59⋊C4—22no—
86C2×Dic59⋊C4—22no—
87C2×Dic59⋊C4—22no—
88C2×Dic59⋊C4—22no—
89C2×Dic59⋊C4—41no—
90C2×Dic59⋊C4—41no—
91C2×Dic59⋊C4—41no—
92C2×Dic59⋊C4C2×C414yes—
93C2×Dic59⋊C4C2×C414yes—
94C2×Dic59⋊C4D414yes—
95C2×Dic59⋊C4D414yes—
96C2×(C2×D59)⋊C4—22no—
97C2×(C2×D59)⋊C4—22no—
98C2×(C2×D59)⋊C4—22no—
99C2×(C2×D59)⋊C4—22no—
100C2×(C2×D59)⋊C4—22no—
101C2×(C2×D59)⋊C4—22no—
102C2×(C2×D59)⋊C4—22no—
103C2×(C2×D59)⋊C4—22no—
104C2×(C2×D59)⋊C4—22no—
105C2×(C2×D59)⋊C4—41no—
106C2×(C2×D59)⋊C4—41no—
107C2×(C2×D59)⋊C4—41no—
108C2×(C2×D59)⋊C4—41no—
109C2×(C2×D59)⋊C4—41no—
110C2×(C2×D59)⋊C4—41no—
111C2×(C2×D59)⋊C4C2×C414yes—
112C2×(C2×D59)⋊C4C2×C414yes—
113C2×(C2×D59)⋊C4Q814yescomplemented
114C2×C4×Dic59—22no—
115C2×C4×Dic59—22no—
116C2×C4×Dic59—22no—
117C2×C4×Dic59—41no—
118C2×C4×Dic59—41no—
119C2×C4×Dic59—41no—
120C59⋊#95—22no—
121C59⋊#95—22no—
122C59⋊#95—22no—
123C59⋊#95—22no—
124C59⋊#95—22no—
125C59⋊#95—22no—
126C59⋊#95—22no—
127C59⋊#95—22no—
128C59⋊#95—22no—
129C59⋊#95—41no—
130C59⋊#95—41no—
131C59⋊#95—41no—
132C59⋊#95D414yes—
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C23×C4×C59C2311yescharacteristic
136C23×C4×C59C2311yescharacteristic
137C23×C4×C59C2311yescharacteristic
138C23×C4×C59C2311yescharacteristic
139C23×C4×C59C2311yescharacteristic
140C2×C4⋊C4×C59—22no—
141C2×C4⋊C4×C59—22no—
142C2×C4⋊C4×C59—22no—
143C2×C4⋊C4×C59—22no—
144C2×C4⋊C4×C59—41no—
145C2×C4⋊C4×C59C2×C414yes—
146#95×C59—22no—
147#95×C59—22no—
148#95×C59—41no—
149#95×C59—41no—
150#95×C59—41no—
151C24×C59C2411yescharacteristic
152C23×D59—21no—
153C23×D59—21no—
154C23×D59—21no—
155C23×D59—21no—
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×D59C22×C412yes—
165C23×D59C2×Q812yes—
166C23×D59#4112yes—
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×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×C59C22×C412yes—
212C22×C4×C59C2×D412yes—
213C22×C4×C59C2×D412yes—
214C22×C4×C59C2×D412yes—
215C22×C4×C59C2×Q812yes—
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×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×Dic59C22×C412yes—
255C22×Dic59C22×C412yes—
256C22×Dic59C22×C412yes—
257C22×Dic59C2×D412yes—
258C22×Dic59C2×D412yes—
259C22×Dic59C2×D412yes—
260C22×Dic59C2×D412yes—
261C22×Dic59C2×D412yes—
262C22×Dic59C2×D412yes—
263C22×Dic59C2×Q812yes—
264C22×Dic59#4112yes—
265C2×C4×D59—28no—
266C2×C4×D59—28no—
267C2×C4×D59—44no—
268C2×C4×D59—44no—
269C2×C4×D59—44no—
270C2×C4×D59—44no—
271C2×C4×D59—44no—
272C2×Dic118—28no—
273C2×Dic118—28no—
274C2×Dic118—44no—
275C2×Dic118—44no—
276C2×Dic118—44no—
277C2×Dic118—44no—
278C2×Dic118—44no—
279C4⋊C4×C59—28no—
280C4⋊C4×C59—44no—
281(C2×D59)⋊C4—28no—
282(C2×D59)⋊C4—28no—
283(C2×D59)⋊C4—44no—
284(C2×D59)⋊C4—44no—
285(C2×D59)⋊C4—44no—
286(C2×D59)⋊C4—44no—
287C4⋊Dic59—44no—
288Dic59⋊C4—28no—
289Dic59⋊C4—44no—
290Dic59⋊C4—44no—
291Dic59⋊C4C22⋊C4116yescomplemented
292C4×Dic59—44no—
293C4×Dic59—44no—
294C23×C59C23×C411yescharacteristic
295C23×C59C22×D411yescharacteristic
296C23×C59C22×D411yescharacteristic
297C23×C59C22×D411yescharacteristic
298C23×C59C22×Q811yescharacteristic
299C23×C59C2×#4111yescharacteristic
300C23×C59C2×#4111yescharacteristic
301C23×C59H(5,𝔽2)11yescharacteristic
302C23×C59H(5,𝔽2)11yescharacteristic
303C23×C59H(5,𝔽2)11yescharacteristic
304C23×C59H(5,𝔽2)11yescharacteristic
305C23×C592−1+411yescharacteristic
306C23×C592−1+411yescharacteristic
307C23×C592−1+411yescharacteristic
308C23×C592−1+411yescharacteristic
309C22×D59—22no—
310C22×D59—22no—
311C22×D59—22no—
312C22×D59—22no—
313C22×D59—22no—
314C22×D59—22no—
315C22×D59—22no—
316C22×D59—22no—
317C22×D59—22no—
318C22×D59—22no—
319C22×D59—22no—
320C22×D59—22no—
321C22×D59—22no—
322C22×D59—22no—
323C22×D59—22no—
324C22×D59—22no—
325C22×D59—22no—
326C22×D59—22no—
327C22×D59—41no—
328C22×D59—41no—
329C22×D59—41no—
330C22×D59—41no—
331C22×D59—41no—
332C22×D59—41no—
333C22×D59—41no—
334C22×D59—41no—
335C22×D59—41no—
336C22×D59—41no—
337C22×D59—41no—
338C22×D59—41no—
339C22×D59—41no—
340C22×D59—41no—
341C22×D59—41no—
342C22×D59—41no—
343C22×D59C4×Q814yes—
344C2×C4×C59—22no—
345C2×C4×C59—22no—
346C2×C4×C59—22no—
347C2×C4×C59—22no—
348C2×C4×C59—22no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
351C2×C4×C59—22no—
352C2×C4×C59—22no—
353C2×C4×C59—22no—
354C2×C4×C59—22no—
355C2×C4×C59—22no—
356C2×C4×C59—22no—
357C2×C4×C59—22no—
358C2×C4×C59—22no—
359C2×C4×C59—22no—
360C2×C4×C59—22no—
361C2×C4×C59—22no—
362C2×C4×C59—41no—
363C2×C4×C59—41no—
364C2×C4×C59—41no—
365C2×C4×C59—41no—
366C2×C4×C59—41no—
367C2×C4×C59—41no—
368C2×C4×C59—41no—
369C2×C4×C59—41no—
370C2×C4×C59—41no—
371C2×C4×C59—41no—
372C2×C4×C59—41no—
373C2×C4×C59—41no—
374C2×C4×C59—41no—
375C2×C4×C59—41no—
376C2×C4×C59—41no—
377C2×C4×C59—41no—
378C2×C4×C59—41no—
379C2×C4×C59—41no—
380C2×C4×C59—41no—
381C2×C4×C59—41no—
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×C59C2×C22⋊C414yes—
393C2×Dic59—22no—
394C2×Dic59—22no—
395C2×Dic59—22no—
396C2×Dic59—22no—
397C2×Dic59—22no—
398C2×Dic59—22no—
399C2×Dic59—22no—
400C2×Dic59—22no—
401C2×Dic59—22no—
402C2×Dic59—22no—
403C2×Dic59—22no—
404C2×Dic59—22no—
405C2×Dic59—22no—
406C2×Dic59—22no—
407C2×Dic59—22no—
408C2×Dic59—22no—
409C2×Dic59—22no—
410C2×Dic59—22no—
411C2×Dic59—22no—
412C2×Dic59—22no—
413C2×Dic59—22no—
414C2×Dic59—22no—
415C2×Dic59—22no—
416C2×Dic59—22no—
417C2×Dic59—41no—
418C2×Dic59—41no—
419C2×Dic59—41no—
420C2×Dic59—41no—
421C2×Dic59—41no—
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×Dic59C2×C22⋊C414yes—
440C2×Dic59C2×C22⋊C414yes—
441C2×Dic59C4×D414yes—
442C4×D59—416no—
443Dic118—416no—
444#14362—591nomaximal, Sylow
445C22×C59C22×C22⋊C411yescharacteristic
446C22×C59C2×C4×D411yescharacteristic
447C22×C59C2×C4×Q811yescharacteristic
448C22×C59#51811yescharacteristic
449C22×C59#51911yescharacteristic
450C22×C59#52011yescharacteristic
451C22×C59#52011yescharacteristic
452C22×C59#53511yescharacteristic
453C22×C59#53611yescharacteristic
454C22×C59#53611yescharacteristic
455C22×C59#53711yescharacteristic
456C22×C59#53711yescharacteristic
457C22×C59#53711yescharacteristic
458C22×C59#53811yescharacteristic
459C22×C59#53911yescharacteristic
460C22×C59#54111yescharacteristic
461C22×C59#54211yescharacteristic
462C22×C59#54311yescharacteristic
463C22×C59#54411yescharacteristic
464C22×C59D4211yescharacteristic
465C22×C59D4211yescharacteristic
466C22×C59#54611yescharacteristic
467C22×C59#54611yescharacteristic
468C22×C59#54611yescharacteristic
469C22×C59#54811yescharacteristic
470C22×C59#54811yescharacteristic
471C22×C59D4×Q811yescharacteristic
472C22×C59D4×Q811yescharacteristic
473C22×C59D4×Q811yescharacteristic
474C22×C59#55211yescharacteristic
475C22×C59#55411yescharacteristic
476C22×C59#56211yescharacteristic
477C22×C59#56211yescharacteristic
478C22×C59#56311yescharacteristic
479C22×C59#56311yescharacteristic
480C2×D59—24no—
481C2×D59—24no—
482C2×D59—24no—
483C2×D59—42no—
484C2×D59—42no—
485C2×D59—42no—
486C2×D59—42no—
487C2×D59—42no—
488C2×D59—42no—
489C2×D59—42no—
490C2×D59—42no—
491C2×D59—42no—
492C2×D59—42no—
493C2×D59—42no—
494C2×D59—42no—
495C4×C59—24no—
496C4×C59—42no—
497C4×C59—42no—
498C4×C59—42no—
499C4×C59—42no—
500C4×C59—81no—
501C4×C59—81no—
502Dic59—24no—
503Dic59—24no—
504Dic59—24no—
505Dic59—42no—
506Dic59—42no—
507Dic59—81no—
508Dic59—81no—
509C22×C22⋊Q8—591no—
510C2×#391—591no—
511C2×#389—591no—
512C2×#387—591no—
513C2×#380—591no—
514#1446—591no—
515#1441—591no—
516#1441—591no—
517#1441D5911yescharacteristic, complemented
518#1439—591no—
519#1439—591no—
520#1437—591no—
521#1437—591no—
522#1436—591no—
523C22⋊#95—591no—
524C2×C59#231111yescharacteristic
525C2×C59#232311yescharacteristic
526C2×C59#232911yescharacteristic
527C2×C59D4×C22⋊C411yescharacteristic
528C2×C59Q8×C22⋊C411yescharacteristic
529C2×C59#236011yescharacteristic
530C2×C59#237811yescharacteristic
531C2×C59#267611yescharacteristic
532C2×C59#267711yescharacteristic
533C2×C59#268111yescharacteristic
534C2×C59#268311yescharacteristic
535C2×C59#269011yescharacteristic
536C2×C59#269211yescharacteristic
537C2×C59#270211yescharacteristic
538C2×C59#270411yescharacteristic
539D59—44no—
540C23×Q8—591no—
541C24×C4—591no—
542C2×C22⋊Q8—598no—
543C2×C22⋊Q8—1184no—
544C2×C22⋊Q8—1184no—
545C22×C4⋊C4—591no—
546C22×C4⋊C4—591no—
547C22×C4⋊C4—591no—
548C22×C4⋊C4—591no—
549C22×C4⋊C4—591no—
550C22×C4⋊C4C2×D5911yescharacteristic
551C22×C4⋊C4C2×D5911yescharacteristic
552C22×C22⋊C4—591no—
553C22×C22⋊C4—591no—
554C22×C22⋊C4—591no—
555C22×C22⋊C4—591no—
556C22×C22⋊C4—591no—
557C22×C22⋊C4—591no—
558C22×C42—591no—
559C22×C42—591no—
560#391—1184no—
561#389—1184no—
562#387—1184no—
563#380—1184no—
564C2×#95—591no—
565C2×#95—591no—
566C2×#95—591no—
567C2×#95—591no—
568C2×#95—591no—
569C2×#95—591no—
570C2×#95—591no—
571C2×#95—591no—
572C2×#95—591no—
573C2×#95—591no—
574C2×#95—591no—
575C2×#95—591no—
576C2×#95—591no—
577C2×#95C2×D5911yescharacteristic
578C2×#95C2×D5911yescharacteristic
579C2×#95C2×D5911yescharacteristic
580C2×#95C2×D5911yescharacteristic
581C2×#95C2×D5911yescharacteristic
582C59#1436211yescharacteristic, complemented, Sylow
583C25—591no—
584C22×Q8—594no—
585C22×Q8—1182no—
586C22×Q8—1182no—
587C22×Q8—1182no—
588C22×Q8—1182no—
589C22×Q8—2361no—
590C22×Q8—2361no—
591C23×C4—591no—
592C23×C4—591no—
593C23×C4—591no—
594C23×C4—591no—
595C23×C4—591no—
596C23×C4—594no—
597C23×C4—591no—
598C23×C4—591no—
599C23×C4—1182no—
600C23×C4—1182no—
601C23×C4—1182no—
602C23×C4—1182no—
603C23×C4—2361no—
604C23×C4—2361no—
605C23×C4C22×D5911yescharacteristic
606C23×C4C22×D5911yescharacteristic
607C23×C4C22×D5911yescharacteristic
608C23×C4C22×D5911yescharacteristic
609C23×C4C22×D5911yescharacteristic
610C23×C4C22×D5911yescharacteristic
611C23×C4C22×D5911yescharacteristic
612C22⋊Q8—11832no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—22no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—594no—
619C2×C4⋊C4—594no—
620C2×C4⋊C4—594no—
621C2×C4⋊C4—594no—
622C2×C4⋊C4—1182no—
623C2×C4⋊C4—1182no—
624C2×C4⋊C4—1182no—
625C2×C4⋊C4—1182no—
626C2×C4⋊C4—1182no—
627C2×C4⋊C4—1182no—
628C2×C4⋊C4—1182no—
629C2×C4⋊C4—2361no—
630C2×C4⋊C4—2361no—
631C2×C4⋊C4—2361no—
632C2×C4⋊C4—2361no—
633C2×C4⋊C4C4×D5914yes—
634C2×C22⋊C4—594no—
635C2×C22⋊C4—594no—
636C2×C22⋊C4—594no—
637C2×C22⋊C4—1182no—
638C2×C22⋊C4—1182no—
639C2×C22⋊C4—1182no—
640C2×C22⋊C4—1182no—
641C2×C22⋊C4—1182no—
642C2×C22⋊C4—1182no—
643C2×C22⋊C4—1182no—
644C2×C22⋊C4—1182no—
645C2×C22⋊C4—1182no—
646C2×C22⋊C4—2361no—
647C2×C22⋊C4—2361no—
648C2×C22⋊C4—2361no—
649C2×C22⋊C4—2361no—
650C2×C22⋊C4—2361no—
651C2×C22⋊C4—2361no—
652C2×C42—1182no—
653C2×C42—1182no—
654C2×C42—1182no—
655C2×C42—2361no—
656C2×C42—2361no—
657C2×C42—2361no—
658#95—22no—
659#95—22no—
660#95—41no—
661#95—41no—
662#95—41no—
663#95—594no—
664#95—1182no—
665#95—1182no—
666#95—1182no—
667#95—1182no—
668#95—1182no—
669#95—1182no—
670#95—1182no—
671#95—1182no—
672#95—1182no—
673#95—2361no—
674#95—2361no—
675#95—2361no—
676C24—592no—
677C24—592no—
678C24—592no—
679C24—1181no—
680C24—1181no—
681C24—1181no—
682C24—1181no—
683C24—1181no—
684C24—1181no—
685C24—1181no—
686C24—1181no—
687C24—1181no—
688C24—1181no—
689C24—1181no—
690C24—1181no—
691C24C23×D5911yescharacteristic
692C2×Q8—1188no—
693C2×Q8—1188no—
694C2×Q8—2364no—
695C2×Q8—2364no—
696C2×Q8—2364no—
697C2×Q8—2364no—
698C2×Q8—2364no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—592no—
742C22×C4—592no—
743C22×C4—592no—
744C22×C4—592no—
745C22×C4—592no—
746C22×C4—592no—
747C22×C4—592no—
748C22×C4—592no—
749C22×C4—592no—
750C22×C4—592no—
751C22×C4—592no—
752C22×C4—1188no—
753C22×C4—1181no—
754C22×C4—1181no—
755C22×C4—1181no—
756C22×C4—1181no—
757C22×C4—1181no—
758C22×C4—1181no—
759C22×C4—1181no—
760C22×C4—1181no—
761C22×C4—1181no—
762C22×C4—1181no—
763C22×C4—1181no—
764C22×C4—1181no—
765C22×C4—1181no—
766C22×C4—1181no—
767C22×C4—1181no—
768C22×C4—1181no—
769C22×C4—1181no—
770C22×C4—1181no—
771C22×C4—1181no—
772C22×C4—1181no—
773C22×C4—1181no—
774C22×C4—1181no—
775C22×C4—1181no—
776C22×C4—1181no—
777C22×C4—1188no—
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—2364no—
793C22×C4—2364no—
794C22×C4—2364no—
795C22×C4—2364no—
796C22×C4—2364no—
797C22×C4C2×C4×D5912yes—
798C22×C4C2×C4×D5912yes—
799C22×C4C2×C4×D5912yes—
800C22×C4D4×D5912yes—
801C22×C4D4×D5912yes—
802C22×C4D4×D5912yes—
803C22×C4Q8×D5912yes—
804C4⋊C4—28no—
805C4⋊C4—44no—
806C4⋊C4—5916no—
807C4⋊C4—1188no—
808C4⋊C4—2364no—
809C4⋊C4—2364no—
810C4⋊C4—2364no—
811C22⋊C4—1188no—
812C22⋊C4—1188no—
813C22⋊C4—2364no—
814C22⋊C4—2364no—
815C22⋊C4—2364no—
816C22⋊C4—2364no—
817C42—2364no—
818C42—2364no—
819C23—594no—
820C23—1182no—
821C23—1182no—
822C23—1182no—
823C23—1182no—
824C23—1182no—
825C23—1182no—
826C23—1182no—
827C23—1182no—
828C23—1182no—
829C23—1182no—
830C23—1182no—
831C23—1182no—
832C23—1182no—
833C23—1182no—
834C23—1182no—
835C23—1182no—
836C23—1182no—
837C23—1182no—
838C23—2361no—
839C23—2361no—
840C23—2361no—
841C23—2361no—
842C23—2361no—
843C23—2361no—
844C23—2361no—
845C23—2361no—
846C23—2361no—
847C23—2361no—
848C23—2361no—
849C23—2361no—
850C23—2361no—
851C23—2361no—
852C23—2361no—
853C23—2361no—
854C23C22×C4×D5911yescharacteristic
855C23C2×D4×D5911yescharacteristic
856C23C2×D4×D5911yescharacteristic
857C23C2×D4×D5911yescharacteristic
858C23C2×Q8×D5911yescharacteristic
859C23#41×D5911yescharacteristic
860C23#41×D5911yescharacteristic
861C23#1427377211yescharacteristic
862C23#1427377211yescharacteristic
863C23#1427377311yescharacteristic
864C23#1427377311yescharacteristic
865C23#1427377411yescharacteristic
866C23#1427377411yescharacteristic
867C23#1427377511yescharacteristic
868C23#1427377511yescharacteristic
869Q8—23616no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—594no—
919C2×C4—594no—
920C2×C4—594no—
921C2×C4—1182no—
922C2×C4—1182no—
923C2×C4—1182no—
924C2×C4—1182no—
925C2×C4—1182no—
926C2×C4—1182no—
927C2×C4—1182no—
928C2×C4—1182no—
929C2×C4—1182no—
930C2×C4—1182no—
931C2×C4—1182no—
932C2×C4—1182no—
933C2×C4—1182no—
934C2×C4—1182no—
935C2×C4—1182no—
936C2×C4—1182no—
937C2×C4—1182no—
938C2×C4—1182no—
939C2×C4—1182no—
940C2×C4—1182no—
941C2×C4—1182no—
942C2×C4—1182no—
943C2×C4—1182no—
944C2×C4—1182no—
945C2×C4—23616no—
946C2×C4—2361no—
947C2×C4—2361no—
948C2×C4—2361no—
949C2×C4—2361no—
950C2×C4—2361no—
951C2×C4—2361no—
952C2×C4—2361no—
953C2×C4—2361no—
954C2×C4—2361no—
955C2×C4—2361no—
956C2×C4—2361no—
957C2×C4—2361no—
958C2×C4—2361no—
959C2×C4—2361no—
960C2×C4—2361no—
961C2×C4—2361no—
962C2×C4—2361no—
963C2×C4—2361no—
964C2×C4—2361no—
965C2×C4—2361no—
966C2×C4—2361no—
967C2×C4—2361no—
968C2×C4C22⋊C4×D5914yes—
969C22—1184no—
970C22—1184no—
971C22—1184no—
972C22—2362no—
973C22—2362no—
974C22—2362no—
975C22—2362no—
976C22—2362no—
977C22—2362no—
978C22—2362no—
979C22—2362no—
980C22—2362no—
981C22—2362no—
982C22—2362no—
983C22—2362no—
984C22C2×C22⋊C4×D5911yescharacteristic
985C22C4×D4×D5911yescharacteristic
986C22C4×Q8×D5911yescharacteristic
987C22#1683787411yescharacteristic
988C22#1683787811yescharacteristic
989C22#1683788211yescharacteristic
990C22#1683788311yescharacteristic
991C22#1683796811yescharacteristic
992C22#1683797511yescharacteristic
993C22#1683797711yescharacteristic
994C22#1683797911yescharacteristic
995C22#1683798111yescharacteristic
996C22#1683798211yescharacteristic
997C22#1683798411yescharacteristic
998C22#1683800011yescharacteristic
999C22#1683801111yescharacteristic
1000C22#1683802211yescharacteristic
1001C22#1683802711yescharacteristic
1002C22#1683802911yescharacteristic
1003C22#1683803411yescharacteristic
1004C22#1683803611yescharacteristic
1005C22#1683804111yescharacteristic
1006C22#1683804411yescharacteristic
1007C22#1683804411yescharacteristic
1008C22#1683806011yescharacteristic
1009C22#1683806211yescharacteristic
1010C22#1683806511yescharacteristic
1011C22#1683806511yescharacteristic
1012C22#1683806711yescharacteristic
1013C22#1683808811yescharacteristic
1014C22#1683810811yescharacteristic
1015C22#1683814911yescharacteristic
1016C22#1683815011yescharacteristic
1017C22#1683815311yescharacteristic
1018C22#1683815411yescharacteristic
1019C4—24no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—42no—
1024C4—81no—
1025C4—81no—
1026C4—1184no—
1027C4—1184no—
1028C4—1184no—
1029C4—4721no—
1030C4—4721no—
1031C4—2362no—
1032C4—2362no—
1033C2—2364no—
1034C2#2142668511yescharacteristic
1035C2#2142677311yescharacteristic
1036C2#2142683011yescharacteristic
1037C2#2142691411yescharacteristic
1038C2#2142693011yescharacteristic
1039C2#2142710411yescharacteristic
1040C2#2142726111yescharacteristic
1041C2#2143039911yescharacteristic
1042C2#2143041011yescharacteristic
1043C2#2143044111yescharacteristic
1044C2#2143046511yescharacteristic
1045C2#2143056411yescharacteristic
1046C2#2143059411yescharacteristic
1047C2#2143073011yescharacteristic
1048C2#2143076011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC59×#1441C2
socle, cosocleC24×C59C24
prime radicalC24×D59C23
hypercenter#1441D59
hypocenterC59#14362
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C2×#16837306C2semidirect
3. C2×#16837297C2semidirect
4. C2×#16837289C2semidirect
6. #21422366C2semidirect
7. #21422349C2semidirect
8. #21422347C2semidirect
13. #21422327C2semidirect
15. C59×#1441C2semidirect
20. C2×#14273705C4semidirect
113. C2×(C2×D59)⋊C4Q8semidirect
291. Dic59⋊C4C22⋊C4semidirect
517. #1441D59semidirect
582. C59#14362semidirect

Maximal subgroups

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

subgroupindex
C22×#142737052
C2×#168373062
C2×#168372972
C2×#168372892
C2×#168372592
#214223662
#214223492
#214223472
#214223402
#214223322
#214223272
(C2×D59)⋊#952
C59×#14412
#1436259