Finite Group Databasebeta

← #28511865

Subgroups — #28511865

Order 15104.

2038 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837302C211yesmaximal, characteristic
2C2×#16837302C211yesmaximal, characteristic
3C2×#16837302C211yesmaximal, characteristic
4C2×#16837294C211yesmaximal, characteristic, complemented
5C2×#16837293C211yesmaximal, characteristic, complemented
6C2×#16837290C211yesmaximal, characteristic, complemented
7C2×#16837271C211yesmaximal, characteristic, complemented
8C2×C4×Dic59⋊C4C211yesmaximal, characteristic, complemented
9#21422341C211yesmaximal, characteristic, complemented
10#21422340C211yesmaximal, characteristic, complemented
11#21422339C211yesmaximal, characteristic, complemented
12#21422338C211yesmaximal, characteristic, complemented
13Dic59⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic59C211yesmaximal, characteristic, complemented
15C2×C59×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×Dic59⋊C4C2211yescharacteristic
19C22×Dic59⋊C4C2211yescharacteristic
20C22×Dic59⋊C4C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×C22⋊Dic59C2211yescharacteristic
24C22×C22⋊Dic59C2211yescharacteristic
25C22×C22⋊Dic59C2211yescharacteristic
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
34C22×C4×Dic59C2211yescharacteristic
35C22×C4×Dic59C2211yescharacteristic
36#16837302—24no—
37#16837302—24no—
38#16837302C418yescomplemented
39#16837294—24no—
40#16837293—24no—
41#16837290—24no—
42#16837271—24no—
43C4×Dic59⋊C4—24no—
44C2×C59⋊#95C2211yescharacteristic
45C2×C59⋊#95C2211yescharacteristic
46C2×C59⋊#95C2211yescharacteristic
47C2×C59⋊#95C2211yescharacteristic
48C2×C59⋊#95C2211yescharacteristic
49C2×C59⋊#95C2211yescharacteristic
50C2×C59⋊#95C2211yescharacteristic
51C2×C59⋊#95C2211yescharacteristic
52C22×C4⋊C4×C59C2211yescharacteristic
53C22×C22⋊C4×C59C2211yescharacteristic
54C22×C22⋊C4×C59C2211yescharacteristic
55C22×C22⋊C4×C59C2211yescharacteristic
56C22×C42×C59C2211yescharacteristic
57C59×#388—24no—
58C2×#95×C59C2211yescharacteristic
59C2×#95×C59C2211yescharacteristic
60C24×D59C2311yescharacteristic
61C22×C22⋊D59—22no—
62C22×C22⋊D59—22no—
63C22×C22⋊D59—22no—
64C22×C22⋊D59—22no—
65C22×C22⋊D59—22no—
66C22×C22⋊D59—22no—
67C22×C22⋊D59C2×C414yes—
68C23×Dic59C2311yescharacteristic
69C23×Dic59C2311yescharacteristic
70C23×Dic59C2311yescharacteristic
71C23×Dic59C2311yescharacteristic
72C23×Dic59C2311yescharacteristic
73C23×Dic59C2311yescharacteristic
74C23×Dic59C2311yescharacteristic
75C2×C4⋊Dic59—22no—
76C2×C4⋊Dic59—22no—
77C2×C4⋊Dic59—41no—
78C2×Dic59⋊C4—22no—
79C2×Dic59⋊C4—22no—
80C2×Dic59⋊C4—22no—
81C2×Dic59⋊C4—22no—
82C2×Dic59⋊C4—22no—
83C2×Dic59⋊C4—22no—
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⋊C4C2×C414yes—
92C2×Dic59⋊C4D414yes—
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⋊Dic59—41no—
101C2×C22⋊Dic59C2×C414yes—
102C2×(C2×D59)⋊C4—22no—
103C2×(C2×D59)⋊C4—22no—
104C2×(C2×D59)⋊C4—22no—
105C2×(C2×D59)⋊C4—22no—
106C2×(C2×D59)⋊C4—22no—
107C2×(C2×D59)⋊C4—22no—
108C2×(C2×D59)⋊C4—22no—
109C2×(C2×D59)⋊C4—22no—
110C2×(C2×D59)⋊C4—22no—
111C2×(C2×D59)⋊C4—22no—
112C2×(C2×D59)⋊C4—22no—
113C2×(C2×D59)⋊C4—22no—
114C2×(C2×D59)⋊C4—41no—
115C2×(C2×D59)⋊C4—41no—
116C2×(C2×D59)⋊C4—41no—
117C2×(C2×D59)⋊C4—41no—
118C2×(C2×D59)⋊C4C2×C414yes—
119C2×(C2×D59)⋊C4C2×C414yes—
120C2×C4×Dic59—22no—
121C2×C4×Dic59—22no—
122C2×C4×Dic59—22no—
123C2×C4×Dic59—22no—
124C2×C4×Dic59—22no—
125C2×C4×Dic59—22no—
126C2×C4×Dic59—22no—
127C2×C4×Dic59—22no—
128C2×C4×Dic59—22no—
129C2×C4×Dic59—22no—
130C2×C4×Dic59C2×C414yes—
131C2×C4×Dic59D414yes—
132C59⋊#95—22no—
133C59⋊#95—22no—
134C59⋊#95—22no—
135C59⋊#95—22no—
136C59⋊#95—22no—
137C59⋊#95—22no—
138C59⋊#95—22no—
139C59⋊#95D414yescomplemented
140C25×C59C2311yescharacteristic
141C23×C4×C59C2311yescharacteristic
142C23×C4×C59C2311yescharacteristic
143C23×C4×C59C2311yescharacteristic
144C23×C4×C59C2311yescharacteristic
145C23×C4×C59C2311yescharacteristic
146C23×C4×C59C2311yescharacteristic
147C2×C4⋊C4×C59—22no—
148C2×C4⋊C4×C59—22no—
149C2×C4⋊C4×C59—41no—
150C2×C22⋊C4×C59—22no—
151C2×C22⋊C4×C59—22no—
152C2×C22⋊C4×C59—22no—
153C2×C22⋊C4×C59—22no—
154C2×C22⋊C4×C59—22no—
155C2×C22⋊C4×C59—22no—
156C2×C22⋊C4×C59—22no—
157C2×C22⋊C4×C59—41no—
158C2×C22⋊C4×C59C2×C414yes—
159C2×C42×C59—22no—
160C2×C42×C59—22no—
161C2×C42×C59—22no—
162#95×C59—22no—
163#95×C59D414yescomplemented
164C24×C59—21no—
165C24×C59—21no—
166C24×C59—21no—
167C24×C59—21no—
168C24×C59—21no—
169C24×C59—21no—
170C24×C59—21no—
171C24×C59—21no—
172C24×C59—21no—
173C24×C59—21no—
174C24×C59—21no—
175C24×C59—21no—
176C24×C59—21no—
177C24×C59—21no—
178C24×C59C22×C412yes—
179C24×C59C2411yescharacteristic
180C23×D59—21no—
181C23×D59—21no—
182C23×D59—21no—
183C23×D59—21no—
184C23×D59—21no—
185C23×D59—21no—
186C23×D59—21no—
187C23×D59—21no—
188C23×D59—21no—
189C23×D59—21no—
190C23×D59—21no—
191C23×D59—21no—
192C23×D59—21no—
193C23×D59—21no—
194C23×D59C22×C412yes—
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×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59—21no—
214C22×C4×C59—21no—
215C22×C4×C59—21no—
216C22×C4×C59—21no—
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59—21no—
220C22×C4×C59—21no—
221C22×C4×C59—21no—
222C22×C4×C59—21no—
223C22×C4×C59—21no—
224C22×C4×C59—21no—
225C22×C4×C59—21no—
226C22×C4×C59—21no—
227C22×C4×C59—21no—
228C22×C4×C59C22×C412yes—
229C22×C4×C59C22×C412yes—
230C22×C4×C59C2×D412yes—
231C22×C4×C59C2×D412yes—
232C22×C4×C59C2×D412yes—
233C22×C4×C59C2×D412yes—
234C22×C4×C59C2×D412yes—
235C22×C4×C59C2×D412yes—
236C22×C4×C59#4112yes—
237C2×C22⋊D59—28no—
238C2×C22⋊D59—28no—
239C2×C22⋊D59—28no—
240C2×C22⋊D59—44no—
241C2×C22⋊D59—44no—
242C2×C22⋊D59—44no—
243C2×C22⋊D59—44no—
244C22×Dic59—21no—
245C22×Dic59—21no—
246C22×Dic59—21no—
247C22×Dic59—21no—
248C22×Dic59—21no—
249C22×Dic59—21no—
250C22×Dic59—21no—
251C22×Dic59—21no—
252C22×Dic59—21no—
253C22×Dic59—21no—
254C22×Dic59—21no—
255C22×Dic59—21no—
256C22×Dic59—21no—
257C22×Dic59—21no—
258C22×Dic59—21no—
259C22×Dic59—21no—
260C22×Dic59—21no—
261C22×Dic59—21no—
262C22×Dic59—21no—
263C22×Dic59—21no—
264C22×Dic59—21no—
265C22×Dic59—21no—
266C22×Dic59—21no—
267C22×Dic59—21no—
268C22×Dic59—21no—
269C22×Dic59—21no—
270C22×Dic59—21no—
271C22×Dic59—21no—
272C22×Dic59—21no—
273C22×Dic59—21no—
274C22×Dic59—21no—
275C22×Dic59—21no—
276C22×Dic59—21no—
277C22×Dic59—21no—
278C22×Dic59—21no—
279C22×Dic59C22×C412yes—
280C22×Dic59C22×C412yes—
281C22×Dic59C22×C412yes—
282C22×Dic59C2×D412yes—
283C22×Dic59C2×D412yes—
284C22×Dic59C2×D412yes—
285C22×Dic59C2×D412yes—
286C22×Dic59C2×D412yes—
287C22×Dic59C2×D412yes—
288C22×Dic59#4112yes—
289C22×Dic59#4112yes—
290C22×Dic59#4112yes—
291C22×Dic59#4112yes—
292C22×Dic59#4112yes—
293C4⋊C4×C59—44no—
294C22⋊C4×C59—28no—
295C22⋊C4×C59—44no—
296C22⋊C4×C59—44no—
297C42×C59—44no—
298C22⋊Dic59—28no—
299C22⋊Dic59—44no—
300C22⋊Dic59—44no—
301(C2×D59)⋊C4—28no—
302(C2×D59)⋊C4—28no—
303(C2×D59)⋊C4—44no—
304(C2×D59)⋊C4—44no—
305(C2×D59)⋊C4—44no—
306(C2×D59)⋊C4—44no—
307C4⋊Dic59—44no—
308Dic59⋊C4—28no—
309Dic59⋊C4—28no—
310Dic59⋊C4—44no—
311Dic59⋊C4—44no—
312Dic59⋊C4—44no—
313C4×Dic59—28no—
314C4×Dic59—28no—
315C4×Dic59—44no—
316C4×Dic59—44no—
317C23×C59—22no—
318C23×C59—22no—
319C23×C59—22no—
320C23×C59—22no—
321C23×C59—22no—
322C23×C59—22no—
323C23×C59—22no—
324C23×C59—41no—
325C23×C59—41no—
326C23×C59—41no—
327C23×C59—41no—
328C23×C59—41no—
329C23×C59—41no—
330C23×C59—41no—
331C23×C59—41no—
332C23×C59—41no—
333C23×C59—41no—
334C23×C59—41no—
335C23×C59—41no—
336C23×C59—41no—
337C23×C59—41no—
338C23×C59—41no—
339C23×C59—41no—
340C23×C59—41no—
341C23×C59—41no—
342C23×C59—41no—
343C23×C59—41no—
344C23×C59—41no—
345C23×C59—41no—
346C23×C59—41no—
347C23×C59—41no—
348C23×C59—41no—
349C23×C59—41no—
350C23×C59—41no—
351C23×C59—41no—
352C23×C59C23×C411yescharacteristic
353C23×C59C22×D411yescharacteristic
354C23×C59C22×D411yescharacteristic
355C23×C59C22×D411yescharacteristic
356C23×C59C22×D411yescharacteristic
357C23×C59C2×#4111yescharacteristic
358C23×C59C2×#4111yescharacteristic
359C23×C59C2×#4111yescharacteristic
360C23×C59C2×#4111yescharacteristic
361C23×C59C2×#4111yescharacteristic
362C23×C59C2×#4111yescharacteristic
363C23×C59H(5,𝔽2)11yescharacteristic
364C23×C59H(5,𝔽2)11yescharacteristic
365C23×C592−1+411yescharacteristic
366C23×C592−1+411yescharacteristic
367C22×D59—22no—
368C22×D59—22no—
369C22×D59—22no—
370C22×D59—22no—
371C22×D59—22no—
372C22×D59—22no—
373C22×D59—22no—
374C22×D59—41no—
375C22×D59—41no—
376C22×D59—41no—
377C22×D59—41no—
378C22×D59—41no—
379C22×D59—41no—
380C22×D59—41no—
381C22×D59—41no—
382C22×D59—41no—
383C22×D59—41no—
384C22×D59—41no—
385C22×D59—41no—
386C22×D59—41no—
387C22×D59—41no—
388C22×D59—41no—
389C22×D59—41no—
390C22×D59—41no—
391C22×D59—41no—
392C22×D59—41no—
393C22×D59—41no—
394C22×D59—41no—
395C22×D59—41no—
396C22×D59—41no—
397C22×D59—41no—
398C22×D59—41no—
399C22×D59—41no—
400C22×D59—41no—
401C22×D59—41no—
402C2×C4×C59—22no—
403C2×C4×C59—22no—
404C2×C4×C59—22no—
405C2×C4×C59—22no—
406C2×C4×C59—22no—
407C2×C4×C59—22no—
408C2×C4×C59—22no—
409C2×C4×C59—22no—
410C2×C4×C59—22no—
411C2×C4×C59—22no—
412C2×C4×C59—22no—
413C2×C4×C59—22no—
414C2×C4×C59—22no—
415C2×C4×C59—22no—
416C2×C4×C59—22no—
417C2×C4×C59—22no—
418C2×C4×C59—22no—
419C2×C4×C59—22no—
420C2×C4×C59—22no—
421C2×C4×C59—22no—
422C2×C4×C59—22no—
423C2×C4×C59—41no—
424C2×C4×C59—41no—
425C2×C4×C59—41no—
426C2×C4×C59—41no—
427C2×C4×C59—41no—
428C2×C4×C59—41no—
429C2×C4×C59—41no—
430C2×C4×C59—41no—
431C2×C4×C59—41no—
432C2×C4×C59—41no—
433C2×C4×C59—41no—
434C2×C4×C59—41no—
435C2×C4×C59—41no—
436C2×C4×C59—41no—
437C2×C4×C59—41no—
438C2×C4×C59—41no—
439C2×C4×C59—41no—
440C2×C4×C59—41no—
441C2×C4×C59—41no—
442C2×C4×C59C4×D414yes—
443C2×C4×C59#12714yes—
444C22⋊D59—416no—
445C2×Dic59—22no—
446C2×Dic59—22no—
447C2×Dic59—22no—
448C2×Dic59—22no—
449C2×Dic59—22no—
450C2×Dic59—22no—
451C2×Dic59—22no—
452C2×Dic59—22no—
453C2×Dic59—22no—
454C2×Dic59—22no—
455C2×Dic59—22no—
456C2×Dic59—22no—
457C2×Dic59—22no—
458C2×Dic59—22no—
459C2×Dic59—22no—
460C2×Dic59—22no—
461C2×Dic59—22no—
462C2×Dic59—22no—
463C2×Dic59—41no—
464C2×Dic59—41no—
465C2×Dic59—41no—
466C2×Dic59—41no—
467C2×Dic59—41no—
468C2×Dic59—41no—
469C2×Dic59—41no—
470C2×Dic59—41no—
471C2×Dic59—41no—
472C2×Dic59—41no—
473C2×Dic59—41no—
474C2×Dic59—41no—
475C2×Dic59—41no—
476C2×Dic59—41no—
477C2×Dic59—41no—
478C2×Dic59—41no—
479C2×Dic59—41no—
480C2×Dic59—41no—
481C2×Dic59—41no—
482C2×Dic59—41no—
483C2×Dic59—41no—
484C2×Dic59—41no—
485C2×Dic59—41no—
486C2×Dic59#11714yes—
487C2×Dic59C4×D414yes—
488C2×Dic59C4×D414yes—
489C2×Dic59C4×D414yes—
490C2×Dic59#12114yes—
491C2×Dic59#12314yes—
492C2×Dic59#12414yes—
493C2×Dic59#12614yes—
494#14001—591nomaximal, Sylow
495C22×C59—42no—
496C22×C59—42no—
497C22×C59—42no—
498C22×C59—42no—
499C22×C59—42no—
500C22×C59—42no—
501C22×C59—42no—
502C22×C59—81no—
503C22×C59—81no—
504C22×C59—81no—
505C22×C59—81no—
506C22×C59—81no—
507C22×C59—81no—
508C22×C59—81no—
509C22×C59—81no—
510C22×C59C2×#11711yescharacteristic
511C22×C59C2×C4×D411yescharacteristic
512C22×C59C2×C4×D411yescharacteristic
513C22×C59C2×C4×D411yescharacteristic
514C22×C59C2×C4×D411yescharacteristic
515C22×C59#52011yescharacteristic
516C22×C59#52011yescharacteristic
517C22×C59C2×#12111yescharacteristic
518C22×C59C2×#12311yescharacteristic
519C22×C59C2×#12411yescharacteristic
520C22×C59C2×#12611yescharacteristic
521C22×C59C2×#12711yescharacteristic
522C22×C59#53211yescharacteristic
523C22×C59#53211yescharacteristic
524C22×C59#53211yescharacteristic
525C22×C59#53511yescharacteristic
526C22×C59#53611yescharacteristic
527C22×C59#54211yescharacteristic
528C22×C59#54211yescharacteristic
529C22×C59D4211yescharacteristic
530C22×C59D4211yescharacteristic
531C22×C59#54711yescharacteristic
532C22×C59#54711yescharacteristic
533C22×C59#54711yescharacteristic
534C22×C59#54711yescharacteristic
535C22×C59#54811yescharacteristic
536C22×C59#54811yescharacteristic
537C22×C59#55011yescharacteristic
538C22×C59#55011yescharacteristic
539C22×C59#55311yescharacteristic
540C22×C59#55311yescharacteristic
541C22×C59#55511yescharacteristic
542C22×C59#55511yescharacteristic
543C22×C59#55611yescharacteristic
544C22×C59#55611yescharacteristic
545C2×D59—42no—
546C2×D59—42no—
547C2×D59—42no—
548C2×D59—42no—
549C2×D59—42no—
550C2×D59—42no—
551C2×D59—42no—
552C2×D59—81no—
553C2×D59—81no—
554C2×D59—81no—
555C2×D59—81no—
556C2×D59—81no—
557C2×D59—81no—
558C2×D59—81no—
559C2×D59—81no—
560C4×C59—24no—
561C4×C59—24no—
562C4×C59—42no—
563C4×C59—42no—
564C4×C59—42no—
565C4×C59—81no—
566Dic59—24no—
567Dic59—42no—
568Dic59—42no—
569Dic59—42no—
570Dic59—42no—
571Dic59—81no—
572Dic59#38818yescomplemented
573C2×#390—591no—
574C2×#390—591no—
575C2×#390—591no—
576C2×#388—591no—
577C2×#388—591no—
578C2×#388—591no—
579C2×#388D5911yescharacteristic, complemented
580C2×#384—591no—
581C2×C4×C4⋊C4—591no—
582#1439—591no—
583#1439—591no—
584#1439—591no—
585#1439—591no—
586C4⋊#95—591no—
587C4×#95—591no—
588C2×C59—82no—
589C2×C59C2×#38811yescharacteristic
590C2×C59C4×#12711yescharacteristic
591C2×C59#232611yescharacteristic
592C2×C59#235411yescharacteristic
593C2×C59#235411yescharacteristic
594C2×C59#236111yescharacteristic
595C2×C59#236111yescharacteristic
596C2×C59#249111yescharacteristic
597C2×C59#249111yescharacteristic
598C2×C59#250011yescharacteristic
599C2×C59#250111yescharacteristic
600C2×C59#251211yescharacteristic
601C2×C59#251211yescharacteristic
602C2×C59#254111yescharacteristic
603C2×C59#254511yescharacteristic
604D59—82no—
605C23×D4—591no—
606C22×C4⋊C4—591no—
607C22×C4⋊C4—591no—
608C22×C4⋊C4—591no—
609C22×C4⋊C4—591no—
610C22×C4⋊C4—591no—
611C22×C4⋊C4—591no—
612C22×C4⋊C4C2×D5911yescharacteristic
613C22×C22⋊C4—591no—
614C22×C22⋊C4—591no—
615C22×C22⋊C4—591no—
616C22×C22⋊C4—591no—
617C22×C22⋊C4—591no—
618C22×C22⋊C4—591no—
619C22×C22⋊C4—591no—
620C22×C22⋊C4—591no—
621C22×C22⋊C4—591no—
622C22×C22⋊C4C2×D5911yescharacteristic
623C22×C22⋊C4C2×D5911yescharacteristic
624C22×C22⋊C4C2×D5911yescharacteristic
625C22×C42—591no—
626C22×C42—591no—
627C22×C42—591no—
628C22×C42—591no—
629C22×C42C2×D5911yescharacteristic
630#390—598no—
631#390—1184no—
632#390—1184no—
633#388—24no—
634#388—1184no—
635#388—1184no—
636#388—1184no—
637#384—1184no—
638C4×C4⋊C4—1184no—
639C2×#95—591no—
640C2×#95—591no—
641C2×#95—591no—
642C2×#95—591no—
643C2×#95—591no—
644C2×#95—591no—
645C2×#95—591no—
646C2×#95—591no—
647C2×#95C2×D5911yescharacteristic
648C2×#95C2×D5911yescharacteristic
649C59#1400111yescharacteristic, complemented, Sylow
650C25—591no—
651C25C22×D5911yescharacteristic
652C22×D4—594no—
653C22×D4—1182no—
654C22×D4—1182no—
655C22×D4—1182no—
656C22×D4—1182no—
657C22×D4—1182no—
658C22×D4—1182no—
659C23×C4—591no—
660C23×C4—591no—
661C23×C4—591no—
662C23×C4—591no—
663C23×C4—591no—
664C23×C4—591no—
665C23×C4—591no—
666C23×C4C22×D5911yescharacteristic
667C23×C4C22×D5911yescharacteristic
668C23×C4C22×D5911yescharacteristic
669C23×C4C22×D5911yescharacteristic
670C23×C4C22×D5911yescharacteristic
671C23×C4C22×D5911yescharacteristic
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—41no—
675C2×C4⋊C4—594no—
676C2×C4⋊C4—594no—
677C2×C4⋊C4—1182no—
678C2×C4⋊C4—1182no—
679C2×C4⋊C4—1182no—
680C2×C4⋊C4—1182no—
681C2×C4⋊C4—1182no—
682C2×C4⋊C4—1182no—
683C2×C4⋊C4—1182no—
684C2×C4⋊C4—1182no—
685C2×C4⋊C4—1182no—
686C2×C4⋊C4—1182no—
687C2×C4⋊C4—1182no—
688C2×C4⋊C4—1182no—
689C2×C4⋊C4—1182no—
690C2×C4⋊C4—2361no—
691C2×C4⋊C4—2361no—
692C2×C4⋊C4—2361no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—594no—
702C2×C22⋊C4—594no—
703C2×C22⋊C4—594no—
704C2×C22⋊C4—1182no—
705C2×C22⋊C4—1182no—
706C2×C22⋊C4—1182no—
707C2×C22⋊C4—1182no—
708C2×C22⋊C4—1182no—
709C2×C22⋊C4—1182no—
710C2×C22⋊C4—1182no—
711C2×C22⋊C4—1182no—
712C2×C22⋊C4—1182no—
713C2×C22⋊C4—1182no—
714C2×C22⋊C4—1182no—
715C2×C22⋊C4—1182no—
716C2×C22⋊C4—1182no—
717C2×C22⋊C4—1182no—
718C2×C22⋊C4—1182no—
719C2×C22⋊C4—1182no—
720C2×C22⋊C4—1182no—
721C2×C22⋊C4—2361no—
722C2×C22⋊C4—2361no—
723C2×C22⋊C4—2361no—
724C2×C22⋊C4—2361no—
725C2×C22⋊C4—2361no—
726C2×C22⋊C4—2361no—
727C2×C22⋊C4—2361no—
728C2×C22⋊C4C4×D5914yes—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—594no—
733C2×C42—594no—
734C2×C42—1182no—
735C2×C42—1182no—
736C2×C42—1182no—
737C2×C42—1182no—
738C2×C42—1182no—
739C2×C42—1182no—
740C2×C42—1182no—
741C2×C42—1182no—
742C2×C42—1182no—
743C2×C42—1182no—
744#95—22no—
745#95—594no—
746#95—1182no—
747#95—1182no—
748#95—1182no—
749#95—1182no—
750#95—1182no—
751#95—1182no—
752#95—1182no—
753#95C22⋊D5914yescomplemented
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—592no—
769C24—1181no—
770C24—1181no—
771C24—1181no—
772C24—1181no—
773C24—1181no—
774C24—1181no—
775C24—1181no—
776C24—1181no—
777C24—1181no—
778C24—1181no—
779C24—1181no—
780C24—1181no—
781C24—1181no—
782C24—1181no—
783C24C2×C4×D5912yes—
784C24C23×D5911yescharacteristic
785C2×D4—1188no—
786C2×D4—1188no—
787C2×D4—1188no—
788C2×D4—2364no—
789C2×D4—2364no—
790C2×D4—2364no—
791C2×D4—2364no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—592no—
826C22×C4—592no—
827C22×C4—592no—
828C22×C4—592no—
829C22×C4—592no—
830C22×C4—592no—
831C22×C4—592no—
832C22×C4—592no—
833C22×C4—592no—
834C22×C4—592no—
835C22×C4—592no—
836C22×C4—592no—
837C22×C4—592no—
838C22×C4—592no—
839C22×C4—1181no—
840C22×C4—1181no—
841C22×C4—1181no—
842C22×C4—1181no—
843C22×C4—1181no—
844C22×C4—1181no—
845C22×C4—1181no—
846C22×C4—1181no—
847C22×C4—1181no—
848C22×C4—1181no—
849C22×C4—1181no—
850C22×C4—1181no—
851C22×C4—1181no—
852C22×C4—1181no—
853C22×C4—1181no—
854C22×C4—1181no—
855C22×C4—1181no—
856C22×C4—1181no—
857C22×C4—1181no—
858C22×C4—1181no—
859C22×C4—1181no—
860C22×C4—1181no—
861C22×C4—1181no—
862C22×C4—1181no—
863C22×C4—1181no—
864C22×C4—1181no—
865C22×C4—1181no—
866C22×C4—1181no—
867C22×C4—1181no—
868C22×C4—1181no—
869C22×C4—1181no—
870C22×C4—1181no—
871C22×C4—1181no—
872C22×C4—1181no—
873C22×C4—1181no—
874C22×C4C2×C4×D5912yes—
875C22×C4C2×C4×D5912yes—
876C22×C4#1174568512yes—
877C22×C4D4×D5912yes—
878C22×C4D4×D5912yes—
879C22×C4D4×D5912yes—
880C22×C4C2×C22⋊D5912yes—
881C22×C4C2×C22⋊D5912yes—
882C22×C4C2×C22⋊D5912yes—
883C4⋊C4—44no—
884C4⋊C4—1188no—
885C4⋊C4—1188no—
886C4⋊C4—2364no—
887C4⋊C4—2364no—
888C4⋊C4—2364no—
889C4⋊C4—2364no—
890C22⋊C4—28no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—1188no—
894C22⋊C4—1188no—
895C22⋊C4—1188no—
896C22⋊C4—2364no—
897C22⋊C4—2364no—
898C22⋊C4—2364no—
899C22⋊C4—2364no—
900C22⋊C4—2364no—
901C22⋊C4—2364no—
902C42—44no—
903C42—1188no—
904C42—1188no—
905C42—2364no—
906C42—2364no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—1182no—
943C23—1182no—
944C23—1182no—
945C23—1182no—
946C23—1182no—
947C23—1182no—
948C23—1182no—
949C23—2361no—
950C23—2361no—
951C23—2361no—
952C23—2361no—
953C23—2361no—
954C23—2361no—
955C23—2361no—
956C23—2361no—
957C23—2361no—
958C23—2361no—
959C23—2361no—
960C23—2361no—
961C23—2361no—
962C23—2361no—
963C23—2361no—
964C23—2361no—
965C23—2361no—
966C23—2361no—
967C23—2361no—
968C23—2361no—
969C23—2361no—
970C23—2361no—
971C23—2361no—
972C23—2361no—
973C23—2361no—
974C23—2361no—
975C23—2361no—
976C23—2361no—
977C23C22×C4×D5911yescharacteristic
978C23C2×D4×D5911yescharacteristic
979C23C2×D4×D5911yescharacteristic
980C23C2×D4×D5911yescharacteristic
981C23C22×C22⋊D5911yescharacteristic
982C23#41×D5911yescharacteristic
983C23#41×D5911yescharacteristic
984C23#41×D5911yescharacteristic
985C23#41×D5911yescharacteristic
986C23#41×D5911yescharacteristic
987C23C2×#1174568511yescharacteristic
988C23#1427377211yescharacteristic
989C23#1427377311yescharacteristic
990C23#1427377411yescharacteristic
991C23#1427377411yescharacteristic
992D4—23616no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—594no—
1034C2×C4—594no—
1035C2×C4—594no—
1036C2×C4—594no—
1037C2×C4—594no—
1038C2×C4—594no—
1039C2×C4—594no—
1040C2×C4—594no—
1041C2×C4—1182no—
1042C2×C4—1182no—
1043C2×C4—1182no—
1044C2×C4—1182no—
1045C2×C4—1182no—
1046C2×C4—1182no—
1047C2×C4—1182no—
1048C2×C4—1182no—
1049C2×C4—1182no—
1050C2×C4—1182no—
1051C2×C4—1182no—
1052C2×C4—1182no—
1053C2×C4—1182no—
1054C2×C4—1182no—
1055C2×C4—1182no—
1056C2×C4—1182no—
1057C2×C4—1182no—
1058C2×C4—1182no—
1059C2×C4—2361no—
1060C2×C4—2361no—
1061C2×C4—2361no—
1062C2×C4—2361no—
1063C2×C4—2361no—
1064C2×C4—2361no—
1065C2×C4—2361no—
1066C2×C4—2361no—
1067C2×C4—2361no—
1068C2×C4—2361no—
1069C2×C4—2361no—
1070C2×C4—2361no—
1071C2×C4—2361no—
1072C2×C4—2361no—
1073C2×C4—2361no—
1074C2×C4—2361no—
1075C2×C4—2361no—
1076C2×C4—2361no—
1077C2×C4—2361no—
1078C2×C4—2361no—
1079C2×C4—2361no—
1080C2×C4—2361no—
1081C2×C4—2361no—
1082C2×C4C4×C22⋊D5914yes—
1083C2×C4#1427372314yes—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—81no—
1092C22—81no—
1093C22—81no—
1094C22—81no—
1095C22—81no—
1096C22—81no—
1097C22—81no—
1098C22—81no—
1099C22—4721no—
1100C22—4721no—
1101C22—4721no—
1102C22—4721no—
1103C22—4721no—
1104C22—4721no—
1105C22—4721no—
1106C22—4721no—
1107C22—2362no—
1108C22—2362no—
1109C22—2362no—
1110C22—2362no—
1111C22—2362no—
1112C22—2362no—
1113C22—2362no—
1114C22#117×D5911yescharacteristic
1115C22C4×D4×D5911yescharacteristic
1116C22C4×D4×D5911yescharacteristic
1117C22C4×D4×D5911yescharacteristic
1118C22C2×C4×C22⋊D5911yescharacteristic
1119C22#1683788111yescharacteristic
1120C22#1683788211yescharacteristic
1121C22#121×D5911yescharacteristic
1122C22#123×D5911yescharacteristic
1123C22#124×D5911yescharacteristic
1124C22#126×D5911yescharacteristic
1125C22C2×#1427372311yescharacteristic
1126C22#1683794811yescharacteristic
1127C22#1683794911yescharacteristic
1128C22#1683794911yescharacteristic
1129C22#1683796811yescharacteristic
1130C22#1683797411yescharacteristic
1131C22#1683801611yescharacteristic
1132C22#1683801811yescharacteristic
1133C22D4×C22⋊D5911yescharacteristic
1134C22#1683803611yescharacteristic
1135C22#1683805011yescharacteristic
1136C22#1683805011yescharacteristic
1137C22#1683805111yescharacteristic
1138C22#1683805111yescharacteristic
1139C22#1683806011yescharacteristic
1140C22#1683806111yescharacteristic
1141C22#1683807011yescharacteristic
1142C22#1683807111yescharacteristic
1143C22#1683810111yescharacteristic
1144C22#1683810311yescharacteristic
1145C22#1683811411yescharacteristic
1146C22#1683811511yescharacteristic
1147C22#1683811911yescharacteristic
1148C22#1683812011yescharacteristic
1149C4—24no—
1150C4—24no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—81no—
1155C4—598no—
1156C4—1184no—
1157C4—4721no—
1158C4—2362no—
1159C4—2362no—
1160C4—2362no—
1161C4—2362no—
1162C2—82no—
1163C2—4722no—
1164C2#388×D5911yescharacteristic
1165C2C4×#1427372311yescharacteristic
1166C2#2142680511yescharacteristic
1167C2#2142704211yescharacteristic
1168C2#2142704611yescharacteristic
1169C2#2142710911yescharacteristic
1170C2#2142711311yescharacteristic
1171C2#2142845611yescharacteristic
1172C2#2142845811yescharacteristic
1173C2#2142855611yescharacteristic
1174C2#2142856511yescharacteristic
1175C2#2142867911yescharacteristic
1176C2#2142868111yescharacteristic
1177C2#2142903911yescharacteristic
1178C2#2142907411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D59
commutatorC23×C59C23×C4
FittingC2×C59×#388C2
socle, cosocleC24×C59C24
prime radicalC23×C22⋊D59C22
hypercenterC2×#388D59
hypocenterC59#14001
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
4. C2×#16837294C2semidirect
5. C2×#16837293C2semidirect
6. C2×#16837290C2semidirect
7. C2×#16837271C2semidirect
8. C2×C4×Dic59⋊C4C2semidirect
9. #21422341C2semidirect
10. #21422340C2semidirect
11. #21422339C2semidirect
12. #21422338C2semidirect
13. Dic59⋊#95C2semidirect
14. #95×Dic59C2semidirect
15. C2×C59×#388C2semidirect
38. #16837302C4semidirect
139. C59⋊#95D4semidirect
163. #95×C59D4semidirect
572. Dic59#388semidirect
579. C2×#388D59semidirect
649. C59#14001semidirect
753. #95C22⋊D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168373022
C2×#168372942
C2×#168372932
C2×#168372902
C2×#168372712
C2×C4×Dic59⋊C42
#214223412
#214223402
#214223392
#214223382
Dic59⋊#952
#95×Dic592
C2×C59×#3882
#1400159