Finite Group Databasebeta

← #28516664

Subgroups — #28516664

Order 15104.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837298C211yesmaximal, characteristic, complemented
2C2×#16837295C211yesmaximal, characteristic
3C2×#16837295C211yesmaximal, characteristic
4C2×#16837275C211yesmaximal, characteristic
5C2×#16837275C211yesmaximal, characteristic
6C2×#16837271C211yesmaximal, characteristic, complemented
7#21422360C211yesmaximal, characteristic, complemented
8#21422359C211yesmaximal, characteristic, complemented
9#21422355C211yesmaximal, characteristic, complemented
10#21422348C211yesmaximal, characteristic, complemented
11#21422339C211yesmaximal, characteristic
12#21422339C211yesmaximal, characteristic
13#21422327C211yesmaximal, characteristic, complemented
14#21422322C211yesmaximal, characteristic, complemented
15C2×C59×#385C211yesmaximal, characteristic
16C22×C4⋊Dic59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×Dic59⋊C4C2211yescharacteristic
19C22×Dic59⋊C4C2211yescharacteristic
20C22×Dic59⋊C4C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×Dic59⋊C4C2211yescharacteristic
24C22×C22⋊Dic59C2211yescharacteristic
25C22×C22⋊Dic59C2211yescharacteristic
26C22×C22⋊Dic59C2211yescharacteristic
27C22×C22⋊Dic59C2211yescharacteristic
28C22×C4×Dic59C2211yescharacteristic
29C22×C4×Dic59C2211yescharacteristic
30#16837298—24no—
31#16837295—24no—
32#16837295C418yescomplemented
33#16837275—24no—
34#16837275—24no—
35#16837271—24no—
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
47C2×C59⋊#95C2211yescharacteristic
48C2×C59⋊#95C2211yescharacteristic
49C2×C59⋊#95C2211yescharacteristic
50C24×C4×C59C2211yescharacteristic
51C22×C4⋊C4×C59C2211yescharacteristic
52C22×C4⋊C4×C59C2211yescharacteristic
53C22×C22⋊C4×C59C2211yescharacteristic
54C22×C22⋊C4×C59C2211yescharacteristic
55C59×#385—24no—
56C2×#95×C59C2211yescharacteristic
57C2×#95×C59C2211yescharacteristic
58C23×Dic59C2311yescharacteristic
59C23×Dic59C2311yescharacteristic
60C23×Dic59C2311yescharacteristic
61C23×Dic59C2311yescharacteristic
62C23×Dic59C2311yescharacteristic
63C23×Dic59C2311yescharacteristic
64C23×Dic59C2311yescharacteristic
65C23×Dic59C2311yescharacteristic
66C2×C4⋊Dic59—22no—
67C2×C4⋊Dic59—22no—
68C2×C4⋊Dic59—22no—
69C2×C4⋊Dic59—22no—
70C2×C4⋊Dic59—41no—
71C2×C4⋊Dic59C2×C414yescomplemented
72C2×Dic59⋊C4—22no—
73C2×Dic59⋊C4—22no—
74C2×Dic59⋊C4—22no—
75C2×Dic59⋊C4—22no—
76C2×Dic59⋊C4—22no—
77C2×Dic59⋊C4—22no—
78C2×Dic59⋊C4—22no—
79C2×Dic59⋊C4—22no—
80C2×Dic59⋊C4—41no—
81C2×Dic59⋊C4—41no—
82C2×Dic59⋊C4—41no—
83C2×Dic59⋊C4—41no—
84C2×Dic59⋊C4—41no—
85C2×Dic59⋊C4—41no—
86C2×Dic59⋊C4—41no—
87C2×Dic59⋊C4—41no—
88C2×Dic59⋊C4—41no—
89C2×Dic59⋊C4D414yes—
90C2×C22⋊Dic59—22no—
91C2×C22⋊Dic59—22no—
92C2×C22⋊Dic59—22no—
93C2×C22⋊Dic59—22no—
94C2×C22⋊Dic59—22no—
95C2×C22⋊Dic59—22no—
96C2×C22⋊Dic59—22no—
97C2×C22⋊Dic59—22no—
98C2×C22⋊Dic59—41no—
99C2×C22⋊Dic59—41no—
100C2×C22⋊Dic59C2×C414yes—
101C2×C22⋊Dic59C2×C414yes—
102C2×C4×Dic59—22no—
103C2×C4×Dic59—22no—
104C2×C4×Dic59—22no—
105C2×C4×Dic59—22no—
106C2×C4×Dic59—41no—
107C2×C4×Dic59C2×C414yescomplemented
108C59⋊#95—22no—
109C59⋊#95—22no—
110C59⋊#95—22no—
111C59⋊#95—22no—
112C59⋊#95—22no—
113C59⋊#95—22no—
114C59⋊#95—22no—
115C59⋊#95—22no—
116C59⋊#95—41no—
117C59⋊#95—41no—
118C59⋊#95—41no—
119C59⋊#95C2×C414yescomplemented
120C59⋊#95C2×C414yescomplemented
121C59⋊#95D414yes—
122C25×C59C2311yescharacteristic
123C23×C4×C59—22no—
124C23×C4×C59—22no—
125C23×C4×C59—22no—
126C23×C4×C59—41no—
127C23×C4×C59—41no—
128C23×C4×C59—41no—
129C23×C4×C59—41no—
130C23×C4×C59C2311yescharacteristic
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C23×C4×C59C2311yescharacteristic
136C2×C4⋊C4×C59—22no—
137C2×C4⋊C4×C59—22no—
138C2×C4⋊C4×C59—22no—
139C2×C4⋊C4×C59—22no—
140C2×C4⋊C4×C59—41no—
141C2×C4⋊C4×C59—41no—
142C2×C22⋊C4×C59—22no—
143C2×C22⋊C4×C59—41no—
144C2×C22⋊C4×C59—41no—
145C2×C22⋊C4×C59C2×C414yes—
146C2×C22⋊C4×C59D414yes—
147C2×C22⋊C4×C59Q814yes—
148#95×C59—22no—
149#95×C59—22no—
150C24×C59—21no—
151C24×C59—21no—
152C24×C59—21no—
153C24×C59—21no—
154C24×C59—21no—
155C24×C59—21no—
156C24×C59—21no—
157C24×C59—21no—
158C24×C59—21no—
159C24×C59—21no—
160C24×C59—21no—
161C24×C59—21no—
162C24×C59C22×C412yes—
163C24×C59C2×D412yes—
164C24×C59C2×Q812yes—
165C24×C59C2411yescharacteristic
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×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—44no—
201C22×C4×C59—44no—
202C22×C4×C59—44no—
203C22×C4×C59—44no—
204C22×C4×C59—44no—
205C22×C4×C59—44no—
206C22×C4×C59—44no—
207C22×C4×C59C22×C412yes—
208C22×C4×C59C22×C412yes—
209C22×C4×C59C2×D412yes—
210C22×C4×C59C2×D412yes—
211C22×C4×C59C2×D412yes—
212C22×C4×C59C2×D412yes—
213C22×C4×C59C2×Q812yes—
214C22×C4×C59C2×Q812yes—
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×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×Dic59C22×C412yes—
262C22×Dic59C22×C412yes—
263C22×Dic59C22×C412yes—
264C22×Dic59C22×C412yes—
265C22×Dic59C2×D412yes—
266C22×Dic59C2×D412yes—
267C22×Dic59C2×D412yes—
268C22×Dic59C2×D412yes—
269C22×Dic59#4112yes—
270C22×Dic59#4112yes—
271C4⋊C4×C59—44no—
272C4⋊C4×C59—44no—
273C22⋊C4×C59—44no—
274C22⋊C4×C59C4⋊C4116yescomplemented
275C22⋊Dic59—28no—
276C22⋊Dic59—28no—
277C22⋊Dic59—44no—
278C22⋊Dic59—44no—
279C4⋊Dic59—28no—
280C4⋊Dic59—44no—
281Dic59⋊C4—44no—
282Dic59⋊C4—44no—
283Dic59⋊C4—44no—
284Dic59⋊C4—44no—
285Dic59⋊C4—44no—
286Dic59⋊C4—44no—
287C4×Dic59—28no—
288C4×Dic59—44no—
289C23×C59—22no—
290C23×C59—22no—
291C23×C59—22no—
292C23×C59—22no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59—22no—
299C23×C59—22no—
300C23×C59—22no—
301C23×C59—22no—
302C23×C59—22no—
303C23×C59—22no—
304C23×C59—22no—
305C23×C59—22no—
306C23×C59—22no—
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×C59—41no—
321C23×C59—41no—
322C23×C59—41no—
323C23×C59C2×C4⋊C414yes—
324C23×C59C23×C411yescharacteristic
325C23×C59C22×D411yescharacteristic
326C23×C59C22×D411yescharacteristic
327C23×C59C22×D411yescharacteristic
328C23×C59C22×Q811yescharacteristic
329C23×C59C2×#4111yescharacteristic
330C23×C59C2×#4111yescharacteristic
331C23×C59H(5,𝔽2)11yescharacteristic
332C23×C59H(5,𝔽2)11yescharacteristic
333C23×C59H(5,𝔽2)11yescharacteristic
334C23×C59H(5,𝔽2)11yescharacteristic
335C23×C592−1+411yescharacteristic
336C23×C592−1+411yescharacteristic
337C23×C592−1+411yescharacteristic
338C23×C592−1+411yescharacteristic
339C2×C4×C59—22no—
340C2×C4×C59—22no—
341C2×C4×C59—22no—
342C2×C4×C59—22no—
343C2×C4×C59—22no—
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—416no—
358C2×C4×C59—41no—
359C2×C4×C59—41no—
360C2×C4×C59—41no—
361C2×C4×C59—41no—
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×C59C2×C4⋊C414yes—
381C2×C4×C59C2×C4⋊C414yes—
382C2×Dic59—22no—
383C2×Dic59—22no—
384C2×Dic59—22no—
385C2×Dic59—22no—
386C2×Dic59—22no—
387C2×Dic59—22no—
388C2×Dic59—22no—
389C2×Dic59—22no—
390C2×Dic59—22no—
391C2×Dic59—22no—
392C2×Dic59—22no—
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—41no—
407C2×Dic59—41no—
408C2×Dic59—41no—
409C2×Dic59—41no—
410C2×Dic59—41no—
411C2×Dic59—41no—
412C2×Dic59—41no—
413C2×Dic59—41no—
414C2×Dic59—41no—
415C2×Dic59—41no—
416C2×Dic59—41no—
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×Dic59C4×D414yes—
437C2×Dic59C4×D414yes—
438#14405—591nomaximal, Sylow
439C22×C59—24no—
440C22×C59—24no—
441C22×C59—24no—
442C22×C59—42no—
443C22×C59—42no—
444C22×C59—42no—
445C22×C59—42no—
446C22×C59—42no—
447C22×C59—42no—
448C22×C59—42no—
449C22×C59—42no—
450C22×C59—42no—
451C22×C59—42no—
452C22×C59—42no—
453C22×C59—42no—
454C22×C59C22×C4⋊C411yescharacteristic
455C22×C59C2×C4×D411yescharacteristic
456C22×C59C2×C4×D411yescharacteristic
457C22×C59#52011yescharacteristic
458C22×C59#52011yescharacteristic
459C22×C59#52011yescharacteristic
460C22×C59#52011yescharacteristic
461C22×C59#53411yescharacteristic
462C22×C59#53511yescharacteristic
463C22×C59#53511yescharacteristic
464C22×C59#53611yescharacteristic
465C22×C59#53611yescharacteristic
466C22×C59#53611yescharacteristic
467C22×C59#53911yescharacteristic
468C22×C59#53911yescharacteristic
469C22×C59#54211yescharacteristic
470C22×C59#54211yescharacteristic
471C22×C59#54411yescharacteristic
472C22×C59#54411yescharacteristic
473C22×C59D4211yescharacteristic
474C22×C59D4211yescharacteristic
475C22×C59D4211yescharacteristic
476C22×C59#54711yescharacteristic
477C22×C59#54711yescharacteristic
478C22×C59#54711yescharacteristic
479C22×C59#54811yescharacteristic
480C22×C59D4×Q811yescharacteristic
481C22×C59D4×Q811yescharacteristic
482C22×C59#55311yescharacteristic
483C22×C59#55411yescharacteristic
484C22×C59#55411yescharacteristic
485C22×C59#56011yescharacteristic
486C22×C59#56311yescharacteristic
487C22×C59#56311yescharacteristic
488C22×C59#56311yescharacteristic
489C4×C59—24no—
490C4×C59—24no—
491C4×C59—42no—
492C4×C59—42no—
493C4×C59—81no—
494C4×C59—81no—
495Dic59—24no—
496Dic59—24no—
497Dic59—42no—
498Dic59—42no—
499Dic59—42no—
500Dic59—42no—
501Dic59—81no—
502Dic59—81no—
503C2×#389—591no—
504C2×#388—591no—
505C2×#388—591no—
506C2×#385—591no—
507C2×#385—591no—
508C2×#385D5911yescharacteristic
509C2×#384—591no—
510#1444—591no—
511#1444—591no—
512#1442—591no—
513#1441—591no—
514#1439—591no—
515#1439—591no—
516#1436—591no—
517#1434—591no—
518C2×C59—44no—
519C2×C59#231711yescharacteristic
520C2×C59#232211yescharacteristic
521C2×C59#232611yescharacteristic
522C2×C59D4×C4⋊C411yescharacteristic
523C2×C59D4×C4⋊C411yescharacteristic
524C2×C59#236111yescharacteristic
525C2×C59#238311yescharacteristic
526C2×C59#266911yescharacteristic
527C2×C59#267411yescharacteristic
528C2×C59#267711yescharacteristic
529C2×C59#268011yescharacteristic
530C2×C59#271811yescharacteristic
531C2×C59#272011yescharacteristic
532C2×C59#272911yescharacteristic
533C2×C59#279011yescharacteristic
534C24×C4C2×D5911yescharacteristic
535C22×C4⋊C4—591no—
536C22×C4⋊C4—591no—
537C22×C4⋊C4—591no—
538C22×C4⋊C4—591no—
539C22×C4⋊C4—591no—
540C22×C4⋊C4—591no—
541C22×C4⋊C4—591no—
542C22×C4⋊C4—591no—
543C22×C4⋊C4C2×D5911yescharacteristic
544C22×C4⋊C4C2×D5911yescharacteristic
545C22×C22⋊C4—591no—
546C22×C22⋊C4—591no—
547C22×C22⋊C4—591no—
548C22×C22⋊C4—591no—
549C22×C22⋊C4C2×D5911yescharacteristic
550C22×C22⋊C4C2×D5911yescharacteristic
551C22×C42—591no—
552C22×C42—591no—
553#389—1184no—
554#388—598no—
555#388—1184no—
556#385—24no—
557#385—1184no—
558#385—1184no—
559#384—1184no—
560C2×#95—591no—
561C2×#95—591no—
562C2×#95—591no—
563C2×#95—591no—
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×#95C2×D5911yescharacteristic
575C2×#95C2×D5911yescharacteristic
576C59#1440511yescharacteristic, complemented, Sylow
577C25C22×D5911yescharacteristic
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—41no—
582C23×C4—41no—
583C23×C4—41no—
584C23×C4—41no—
585C23×C4—591no—
586C23×C4—591no—
587C23×C4—591no—
588C23×C4—591no—
589C23×C4—591no—
590C23×C4—591no—
591C23×C4—591no—
592C23×C4—591no—
593C23×C4C22×D5911yescharacteristic
594C23×C4C22×D5911yescharacteristic
595C23×C4C22×D5911yescharacteristic
596C23×C4C22×D5911yescharacteristic
597C23×C4C22×D5911yescharacteristic
598C23×C4C22×D5911yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—594no—
606C2×C4⋊C4—594no—
607C2×C4⋊C4—1182no—
608C2×C4⋊C4—1182no—
609C2×C4⋊C4—1182no—
610C2×C4⋊C4—1182no—
611C2×C4⋊C4—1182no—
612C2×C4⋊C4—1182no—
613C2×C4⋊C4—1182no—
614C2×C4⋊C4—1182no—
615C2×C4⋊C4—1182no—
616C2×C4⋊C4—1182no—
617C2×C4⋊C4—1182no—
618C2×C4⋊C4—1182no—
619C2×C4⋊C4—2361no—
620C2×C4⋊C4—2361no—
621C2×C4⋊C4—2361no—
622C2×C4⋊C4—2361no—
623C2×C4⋊C4—2361no—
624C2×C4⋊C4—2361no—
625C2×C4⋊C4—2361no—
626C2×C4⋊C4—2361no—
627C2×C4⋊C4—2361no—
628C2×C4⋊C4—2361no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—41no—
631C2×C22⋊C4—41no—
632C2×C22⋊C4—594no—
633C2×C22⋊C4—594no—
634C2×C22⋊C4—1182no—
635C2×C22⋊C4—1182no—
636C2×C22⋊C4—1182no—
637C2×C22⋊C4—1182no—
638C2×C22⋊C4—1182no—
639C2×C22⋊C4—1182no—
640C2×C22⋊C4—1182no—
641C2×C22⋊C4—1182no—
642C2×C22⋊C4—2361no—
643C2×C22⋊C4—2361no—
644C2×C22⋊C4Dic11814yes—
645C2×C22⋊C4C4×D5914yes—
646C2×C22⋊C4C22⋊D5914yes—
647C2×C42—594no—
648C2×C42—1182no—
649C2×C42—1182no—
650C2×C42—1182no—
651C2×C42—1182no—
652C2×C42—2361no—
653#95—22no—
654#95—22no—
655#95—594no—
656#95—594no—
657#95—594no—
658#95—1182no—
659#95—1182no—
660#95—1182no—
661#95—1182no—
662#95—1182no—
663#95—1182no—
664#95—1182no—
665#95—1182no—
666#95—2361no—
667#95—2361no—
668#95—2361no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C2×Dic11812yes—
682C24C2×C4×D5912yes—
683C24C2×C22⋊D5912yes—
684C24C23×D5911yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
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—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—592no—
727C22×C4—592no—
728C22×C4—592no—
729C22×C4—592no—
730C22×C4—592no—
731C22×C4—592no—
732C22×C4—592no—
733C22×C4—592no—
734C22×C4—592no—
735C22×C4—592no—
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×C4—1181no—
745C22×C4—1181no—
746C22×C4—1181no—
747C22×C4—1181no—
748C22×C4—1181no—
749C22×C4—1181no—
750C22×C4—1181no—
751C22×C4—1181no—
752C22×C4—1181no—
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—1181no—
778C22×C4—1181no—
779C22×C4—1181no—
780C22×C4—1181no—
781C22×C4—1181no—
782C22×C4C2×Dic11812yes—
783C22×C4C2×Dic11812yes—
784C22×C4C2×C4×D5912yes—
785C22×C4C2×C4×D5912yes—
786C22×C4D4×D5912yes—
787C22×C4D4×D5912yes—
788C22×C4C2×C22⋊D5912yes—
789C22×C4C2×C22⋊D5912yes—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C4⋊C4—1188no—
793C4⋊C4—2364no—
794C4⋊C4—2364no—
795C4⋊C4—2364no—
796C4⋊C4—2364no—
797C4⋊C4—2364no—
798C4⋊C4—2364no—
799C4⋊C4—2364no—
800C22⋊C4—44no—
801C22⋊C4—1188no—
802C22⋊C4—1188no—
803C22⋊C4—2364no—
804C22⋊C4—2364no—
805C22⋊C4Dic59⋊C4116yescomplemented
806C42—1188no—
807C42—2364no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×Dic59⋊C414yes—
843C23C22×C4×D5911yescharacteristic
844C23C2×D4×D5911yescharacteristic
845C23C2×D4×D5911yescharacteristic
846C23C22×C22⋊D5911yescharacteristic
847C23C22×Dic11811yescharacteristic
848C23#41×D5911yescharacteristic
849C23#41×D5911yescharacteristic
850C23#1427377211yescharacteristic
851C23#1427377211yescharacteristic
852C23#1427377211yescharacteristic
853C23#1427377211yescharacteristic
854C23#1427377411yescharacteristic
855C23#1427377411yescharacteristic
856C23#1427377511yescharacteristic
857C23#1427377511yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—416no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
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—594no—
900C2×C4—594no—
901C2×C4—1182no—
902C2×C4—1182no—
903C2×C4—1182no—
904C2×C4—1182no—
905C2×C4—1182no—
906C2×C4—1182no—
907C2×C4—1182no—
908C2×C4—1182no—
909C2×C4—1182no—
910C2×C4—1182no—
911C2×C4—1182no—
912C2×C4—1182no—
913C2×C4—1182no—
914C2×C4—1182no—
915C2×C4—1182no—
916C2×C4—1182no—
917C2×C4—1182no—
918C2×C4—1182no—
919C2×C4—1182no—
920C2×C4—1182no—
921C2×C4—1182no—
922C2×C4—1182no—
923C2×C4—1182no—
924C2×C4—1182no—
925C2×C4—2361no—
926C2×C4—2361no—
927C2×C4—2361no—
928C2×C4—2361no—
929C2×C4—2361no—
930C2×C4—2361no—
931C2×C4—2361no—
932C2×C4—2361no—
933C2×C4—2361no—
934C2×C4—2361no—
935C2×C4—2361no—
936C2×C4—2361no—
937C2×C4—2361no—
938C2×C4—2361no—
939C2×C4—2361no—
940C2×C4—2361no—
941C2×C4—2361no—
942C2×C4—2361no—
943C2×C4—2361no—
944C2×C4—2361no—
945C2×C4—2361no—
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×C4C2×Dic59⋊C414yes—
956C2×C4C2×Dic59⋊C414yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×Dic59⋊C411yescharacteristic
973C22C4×D4×D5911yescharacteristic
974C22C4×D4×D5911yescharacteristic
975C22#1683788111yescharacteristic
976C22#1683788111yescharacteristic
977C22#1683788311yescharacteristic
978C22#1683788311yescharacteristic
979C22#1683796211yescharacteristic
980C22#1683796711yescharacteristic
981C22#1683796911yescharacteristic
982C22#1683797511yescharacteristic
983C22#1683797511yescharacteristic
984C22#1683797611yescharacteristic
985C22#1683799511yescharacteristic
986C22#1683799811yescharacteristic
987C22#1683802011yescharacteristic
988C22#1683802211yescharacteristic
989C22#1683803311yescharacteristic
990C22#1683803311yescharacteristic
991C22#1683803411yescharacteristic
992C22D4×C22⋊D5911yescharacteristic
993C22D4×C22⋊D5911yescharacteristic
994C22#1683805111yescharacteristic
995C22#1683805111yescharacteristic
996C22#1683805411yescharacteristic
997C22#1683806211yescharacteristic
998C22D4×Dic11811yescharacteristic
999C22D4×Dic11811yescharacteristic
1000C22#1683809711yescharacteristic
1001C22#1683811111yescharacteristic
1002C22#1683811111yescharacteristic
1003C22#1683814111yescharacteristic
1004C22#1683815311yescharacteristic
1005C22#1683815311yescharacteristic
1006C22#1683815511yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—81no—
1012C4—81no—
1013C4—1184no—
1014C4—1184no—
1015C4—4721no—
1016C4—4721no—
1017C4—2362no—
1018C4—2362no—
1019C4—2362no—
1020C4—2362no—
1021C2—44no—
1022C2#2142672011yescharacteristic
1023C2#2142676311yescharacteristic
1024C2#2142680211yescharacteristic
1025C2D4×Dic59⋊C411yescharacteristic
1026C2D4×Dic59⋊C411yescharacteristic
1027C2#2142711511yescharacteristic
1028C2#2142728411yescharacteristic
1029C2#2143031011yescharacteristic
1030C2#2143037311yescharacteristic
1031C2#2143041111yescharacteristic
1032C2#2143043511yescharacteristic
1033C2#2143094211yescharacteristic
1034C2#2143097711yescharacteristic
1035C2#2143108211yescharacteristic
1036C2#2143186911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#385C2
socle, cosocleC24×C59C24
prime radicalC25×C59C23
hypercenterC2×#385D59
hypocenterC59#14405
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#16837298C2semidirect
6. C2×#16837271C2semidirect
7. #21422360C2semidirect
8. #21422359C2semidirect
9. #21422355C2semidirect
10. #21422348C2semidirect
13. #21422327C2semidirect
14. #21422322C2semidirect
32. #16837295C4semidirect
71. C2×C4⋊Dic59C2×C4semidirect
107. C2×C4×Dic59C2×C4semidirect
119. C59⋊#95C2×C4semidirect
120. C59⋊#95C2×C4semidirect
274. C22⋊C4×C59C4⋊C4semidirect
576. C59#14405semidirect
805. C22⋊C4Dic59⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#168372982
C2×#168372952
C2×#168372752
C2×#168372712
#214223602
#214223592
#214223552
#214223482
#214223392
#214223272
#214223222
C2×C59×#3852
#1440559